#ifndef STAN_MATH_PRIM_SCAL_PROB_RAYLEIGH_CDF_HPP
#define STAN_MATH_PRIM_SCAL_PROB_RAYLEIGH_CDF_HPP

#include <boost/random/uniform_real_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_nonnegative.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/log1m.hpp>
#include <stan/math/prim/scal/fun/square.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <stan/math/prim/scal/meta/length.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/fun/constants.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <stan/math/prim/scal/meta/scalar_seq_view.hpp>
#include <stan/math/prim/scal/meta/VectorBuilder.hpp>
#include <cmath>

namespace stan {
  namespace math {

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

      using stan::is_constant_struct;
      using std::exp;

      T_partials_return cdf(1.0);

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

      check_not_nan(function, "Random variable", y);
      check_nonnegative(function, "Random variable", y);
      check_not_nan(function, "Scale parameter", sigma);
      check_positive(function, "Scale parameter", sigma);
      check_consistent_sizes(function,
                             "Random variable", y,
                             "Scale parameter", sigma);

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

      scalar_seq_view<const T_y> y_vec(y);
      scalar_seq_view<const T_scale> sigma_vec(sigma);
      size_t N = max_size(y, sigma);

      VectorBuilder<true, T_partials_return, T_scale> inv_sigma(length(sigma));
      for (size_t i = 0; i < length(sigma); i++) {
        inv_sigma[i] = 1.0 / value_of(sigma_vec[i]);
      }

      for (size_t n = 0; n < N; n++) {
        const T_partials_return y_dbl = value_of(y_vec[n]);
        const T_partials_return y_sqr = y_dbl * y_dbl;
        const T_partials_return inv_sigma_sqr = inv_sigma[n] * inv_sigma[n];
        const T_partials_return exp_val = exp(-0.5 * y_sqr * inv_sigma_sqr);

        if (include_summand<false, T_y, T_scale>::value)
          cdf *= (1.0 - exp_val);
      }

      for (size_t n = 0; n < N; n++) {
        const T_partials_return y_dbl = value_of(y_vec[n]);
        const T_partials_return y_sqr = square(y_dbl);
        const T_partials_return inv_sigma_sqr = square(inv_sigma[n]);
        const T_partials_return exp_val = exp(-0.5 * y_sqr * inv_sigma_sqr);
        const T_partials_return exp_div_1m_exp = exp_val / (1.0 - exp_val);

        if (!is_constant_struct<T_y>::value)
          operands_and_partials.d_x1[n] += y_dbl * inv_sigma_sqr
            * exp_div_1m_exp * cdf;
        if (!is_constant_struct<T_scale>::value)
          operands_and_partials.d_x2[n] -= y_sqr * inv_sigma_sqr
            * inv_sigma[n] * exp_div_1m_exp * cdf;
      }
      return operands_and_partials.value(cdf);
    }

  }
}
#endif
