#ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_CDF_HPP
#define STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_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/operands_and_partials.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_positive_finite.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/fun/lbeta.hpp>
#include <stan/math/prim/scal/fun/digamma.hpp>
#include <stan/math/prim/scal/fun/lgamma.hpp>
#include <stan/math/prim/scal/fun/binomial_coefficient_log.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <stan/math/prim/scal/meta/scalar_seq_view.hpp>
#include <stan/math/prim/scal/meta/contains_nonconstant_struct.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <stan/math/prim/scal/prob/beta_rng.hpp>
#include <stan/math/prim/scal/fun/F32.hpp>
#include <stan/math/prim/scal/fun/grad_F32.hpp>
#include <cmath>

namespace stan {
  namespace math {

    /**
     * Returns the CDF of the Beta-Binomial distribution with given population 
     * size, prior success, and prior failure parameters. Given containers of 
     * matching sizes, returns the product of probabilities.
     *
     * @tparam T_n type of success parameter
     * @tparam T_N type of population size parameter
     * @tparam T_size1 type of prior success parameter
     * @tparam T_size2 type of prior failure parameter
     * @param n success parameter
     * @param N population size parameter
     * @param alpha prior success parameter
     * @param beta prior failure parameter
     * @return probability or product of probabilities
     * @throw std::domain_error if N, alpha, or beta fails to be positive
     * @throw std::invalid_argument if container sizes mismatch
     */
    template <typename T_n, typename T_N,
              typename T_size1, typename T_size2>
    typename return_type<T_size1, T_size2>::type
    beta_binomial_cdf(const T_n& n, const T_N& N, const T_size1& alpha,
                      const T_size2& beta) {
      static const char* function("beta_binomial_cdf");
      typedef typename stan::partials_return_type<T_n, T_N, T_size1,
                                                  T_size2>::type
        T_partials_return;

      if (!(stan::length(n) && stan::length(N) && stan::length(alpha)
            && stan::length(beta)))
        return 1.0;

      T_partials_return P(1.0);

      check_nonnegative(function, "Population size parameter", N);
      check_positive_finite(function,
                            "First prior sample size parameter", alpha);
      check_positive_finite(function,
                            "Second prior sample size parameter", beta);
      check_consistent_sizes(function,
                             "Successes variable", n,
                             "Population size parameter", N,
                             "First prior sample size parameter", alpha,
                             "Second prior sample size parameter", beta);

      scalar_seq_view<T_n> n_vec(n);
      scalar_seq_view<T_N> N_vec(N);
      scalar_seq_view<T_size1> alpha_vec(alpha);
      scalar_seq_view<T_size2> beta_vec(beta);
      size_t size = max_size(n, N, alpha, beta);

      using std::exp;
      using std::exp;

      operands_and_partials<T_size1, T_size2>
        ops_partials(alpha, beta);

      // Explicit return for extreme values
      // The gradients are technically ill-defined, but treated as zero
      for (size_t i = 0; i < stan::length(n); i++) {
        if (value_of(n_vec[i]) <= 0)
          return ops_partials.build(0.0);
      }

      for (size_t i = 0; i < size; i++) {
        // Explicit results for extreme values
        // The gradients are technically ill-defined, but treated as zero
        if (value_of(n_vec[i]) >= value_of(N_vec[i])) {
          continue;
        }

        const T_partials_return n_dbl = value_of(n_vec[i]);
        const T_partials_return N_dbl = value_of(N_vec[i]);
        const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
        const T_partials_return beta_dbl = value_of(beta_vec[i]);

        const T_partials_return mu = alpha_dbl + n_dbl + 1;
        const T_partials_return nu = beta_dbl + N_dbl - n_dbl - 1;

        const T_partials_return F = F32((T_partials_return)1, mu,
                                        -N_dbl + n_dbl + 1,
                                        n_dbl + 2, 1 - nu,
                                        (T_partials_return)1);

        T_partials_return C = lgamma(nu) - lgamma(N_dbl - n_dbl);
        C += lgamma(mu) - lgamma(n_dbl + 2);
        C += lgamma(N_dbl + 2) - lgamma(N_dbl + alpha_dbl + beta_dbl);
        C = exp(C);

        C *= F / exp(lbeta(alpha_dbl, beta_dbl));
        C /= N_dbl + 1;

        const T_partials_return Pi = 1 - C;

        P *= Pi;

        T_partials_return dF[6];
        T_partials_return digammaOne = 0;
        T_partials_return digammaTwo = 0;

        if (contains_nonconstant_struct<T_size1, T_size2>::value) {
          digammaOne = digamma(mu + nu);
          digammaTwo = digamma(alpha_dbl + beta_dbl);
          grad_F32(dF, (T_partials_return)1, mu, -N_dbl + n_dbl + 1,
                   n_dbl + 2,
                   1 - nu, (T_partials_return)1);
        }
        if (!is_constant_struct<T_size1>::value) {
          const T_partials_return g
            = - C * (digamma(mu) - digammaOne + dF[1] / F
                     - digamma(alpha_dbl) + digammaTwo);
          ops_partials.edge1_.partials_[i]
            += g / Pi;
        }
        if (!is_constant_struct<T_size2>::value) {
          const T_partials_return g
            = - C * (digamma(nu) - digammaOne - dF[4] / F - digamma(beta_dbl)
                     + digammaTwo);
          ops_partials.edge2_.partials_[i]
            += g / Pi;
        }
      }

      if (!is_constant_struct<T_size1>::value) {
        for (size_t i = 0; i < stan::length(alpha); ++i)
          ops_partials.edge1_.partials_[i] *= P;
      }
      if (!is_constant_struct<T_size2>::value) {
        for (size_t i = 0; i < stan::length(beta); ++i)
          ops_partials.edge2_.partials_[i] *= P;
      }

      return ops_partials.build(P);
    }

  }
}
#endif
