#ifndef STAN_MATH_PRIM_SCAL_PROB_NORMAL_CDF_HPP
#define STAN_MATH_PRIM_SCAL_PROB_NORMAL_CDF_HPP

#include <stan/math/prim/scal/meta/is_constant_struct.hpp>
#include <stan/math/prim/scal/meta/partials_return_type.hpp>
#include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
#include <stan/math/prim/scal/meta/scalar_seq_view.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/contains_nonconstant_struct.hpp>
#include <stan/math/prim/scal/meta/max_size.hpp>
#include <boost/random/normal_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <cmath>

namespace stan {
  namespace math {

    /**
     * Calculates the normal cumulative distribution function for the given
     * variate, location, and scale.
     *
     * \f$\Phi(x) = \frac{1}{\sqrt{2 \pi}} \int_{-\inf}^x e^{-t^2/2} dt\f$.
     *
     * @param y A scalar variate.
     * @param mu The location of the normal distribution.
     * @param sigma The scale of the normal distriubtion
     * @return The unit normal cdf evaluated at the specified arguments.
     * @tparam T_y Type of y.
     * @tparam T_loc Type of mean parameter.
     * @tparam T_scale Type of standard deviation paramater.
     */
    template <typename T_y, typename T_loc, typename T_scale>
    typename return_type<T_y, T_loc, T_scale>::type
    normal_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
      static const char* function("normal_cdf");
      typedef typename stan::partials_return_type<T_y, T_loc, T_scale>::type
        T_partials_return;

      using std::exp;

      T_partials_return cdf(1.0);

      if (!(stan::length(y)
            && stan::length(mu)
            && stan::length(sigma)))
        return cdf;

      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);

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

      scalar_seq_view<const T_y> y_vec(y);
      scalar_seq_view<const T_loc> mu_vec(mu);
      scalar_seq_view<const T_scale> sigma_vec(sigma);
      size_t N = max_size(y, mu, sigma);
      const double SQRT_TWO_OVER_PI = std::sqrt(2.0 / 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 cdf_;
        if (scaled_diff < -37.5 * INV_SQRT_2)
          cdf_ = 0.0;
        else if (scaled_diff < -5.0 * INV_SQRT_2)
          cdf_ = 0.5 * erfc(-scaled_diff);
        else if (scaled_diff > 8.25 * INV_SQRT_2)
          cdf_ = 1;
        else
          cdf_ = 0.5 * (1.0 + erf(scaled_diff));

        cdf *= cdf_;

        if (contains_nonconstant_struct<T_y, T_loc, T_scale>::value) {
          const T_partials_return rep_deriv
            = (scaled_diff < -37.5 * INV_SQRT_2)
            ? 0.0
            : SQRT_TWO_OVER_PI * 0.5
            * exp(-scaled_diff * scaled_diff) / cdf_ / sigma_dbl;
          if (!is_constant_struct<T_y>::value)
            operands_and_partials.d_x1[n] += rep_deriv;
          if (!is_constant_struct<T_loc>::value)
            operands_and_partials.d_x2[n] -= rep_deriv;
          if (!is_constant_struct<T_scale>::value)
            operands_and_partials.d_x3[n] -= rep_deriv * scaled_diff * SQRT_2;
        }
      }

      if (!is_constant_struct<T_y>::value) {
        for (size_t n = 0; n < stan::length(y); ++n)
          operands_and_partials.d_x1[n] *= cdf;
      }
      if (!is_constant_struct<T_loc>::value) {
        for (size_t n = 0; n < stan::length(mu); ++n)
          operands_and_partials.d_x2[n] *= cdf;
      }
      if (!is_constant_struct<T_scale>::value) {
        for (size_t n = 0; n < stan::length(sigma); ++n)
          operands_and_partials.d_x3[n] *= cdf;
      }
      return operands_and_partials.value(cdf);
    }

  }
}
#endif
