#ifndef STAN__MATH__PRIM__SCAL__PROB__NORMAL_CDF_LOG_HPP
#define STAN__MATH__PRIM__SCAL__PROB__NORMAL_CDF_LOG_HPP

#include <boost/random/normal_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <stan/math/prim/scal/meta/OperandsAndPartials.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.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <stan/math/prim/scal/meta/constants.hpp>
#include <stan/math/prim/scal/meta/max_size.hpp>
#include <stan/math/prim/scal/meta/contains_nonconstant_struct.hpp>

namespace stan {

  namespace prob {

    template <typename T_y, typename T_loc, typename T_scale>
    typename return_type<T_y,T_loc,T_scale>::type
    normal_cdf_log(const T_y& y, const T_loc& mu, const T_scale& sigma) {
      static const char* function("stan::prob::normal_cdf_log");
      typedef typename stan::partials_return_type<T_y,T_loc,T_scale>::type
        T_partials_return;

      using stan::math::check_positive;
      using stan::math::check_finite;
      using stan::math::check_not_nan;
      using stan::math::check_consistent_sizes;
      using stan::math::value_of;
      using stan::math::INV_SQRT_2;

      T_partials_return cdf_log(0.0);
      // check if any vectors are zero length
      if (!(stan::length(y) 
            && stan::length(mu) 
            && stan::length(sigma)))
        return cdf_log;

      check_not_nan(function, "Random variable", y);
      check_finite(function, "Location parameter", mu);
      check_not_nan(function, "Scale parameter", sigma);
      check_positive(function, "Scale parameter", sigma);
      check_consistent_sizes(function,
                             "Random variable", y,
                             "Location parameter", mu,
                             "Scale parameter", sigma);

      agrad::OperandsAndPartials<T_y, T_loc, T_scale> 
        operands_and_partials(y, mu, sigma);

      VectorView<const T_y> y_vec(y);
      VectorView<const T_loc> mu_vec(mu);
      VectorView<const T_scale> sigma_vec(sigma);
      size_t N = max_size(y, mu, sigma);
    
      const double SQRT_TWO_OVER_PI = std::sqrt(2.0 / stan::math::pi());
      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_dbl = value_of(sigma_vec[n]);

        const T_partials_return scaled_diff = (y_dbl - mu_dbl) 
          / (sigma_dbl * SQRT_2);
        
        T_partials_return one_p_erf;
        if (scaled_diff < -37.5 * INV_SQRT_2)
          one_p_erf = 0.0;
        else if (scaled_diff < -5.0 * INV_SQRT_2)
          one_p_erf =  erfc(-scaled_diff);
        else if (scaled_diff > 8.25 * INV_SQRT_2)
          one_p_erf = 2.0;
        else
          one_p_erf = 1.0 + erf(scaled_diff);

        // log cdf
        cdf_log += LOG_HALF + log(one_p_erf);

        // gradients
        if (contains_nonconstant_struct<T_y, T_loc, T_scale>::value) {
          const T_partials_return rep_deriv_div_sigma
            = scaled_diff < -37.5 * INV_SQRT_2
                            ? std::numeric_limits<double>::infinity()
                            : SQRT_TWO_OVER_PI * exp(-scaled_diff * scaled_diff)
                            / sigma_dbl / one_p_erf;
          if (!is_constant_struct<T_y>::value)
            operands_and_partials.d_x1[n] += rep_deriv_div_sigma;
          if (!is_constant_struct<T_loc>::value)
            operands_and_partials.d_x2[n] -= rep_deriv_div_sigma;
          if (!is_constant_struct<T_scale>::value)
            operands_and_partials.d_x3[n] -= rep_deriv_div_sigma
              * scaled_diff * stan::math::SQRT_2;
        }
      }
      return operands_and_partials.to_var(cdf_log,y,mu,sigma);
    }
  }
}
#endif
