#ifndef STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_LCDF_HPP
#define STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_LCDF_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_bounded.hpp>
#include <stan/math/prim/scal/err/check_finite.hpp>
#include <stan/math/prim/scal/err/check_greater_or_equal.hpp>
#include <stan/math/prim/scal/err/check_less_or_equal.hpp>
#include <stan/math/prim/scal/err/check_nonnegative.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/fun/inv_logit.hpp>
#include <stan/math/prim/scal/fun/log1m.hpp>
#include <stan/math/prim/scal/fun/log_inv_logit.hpp>
#include <stan/math/prim/scal/fun/multiply_log.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <stan/math/prim/scal/fun/binomial_coefficient_log.hpp>
#include <stan/math/prim/scal/fun/lbeta.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/fun/inc_beta.hpp>
#include <boost/random/binomial_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <cmath>
#include <string>

namespace stan {
  namespace math {

    /**
     * Returns the log CDF for the binomial distribution evaluated at the
     * specified success, population size, and chance of success. If given
     * containers of matching lengths, returns the log sum of probabilities.
     *
     * @tparam T_n type of successes parameter
     * @tparam T_N type of population size parameter
     * @tparam theta type of chance of success parameter
     * @param n successes parameter
     * @param N population size parameter
     * @param theta chance of success parameter
     * @return log probability or log sum of probabilities
     * @throw std::domain_error if N is negative
     * @throw std::domain_error if theta is not a valid probability
     * @throw std::invalid_argument if container sizes mismatch
     */
    template <typename T_n, typename T_N, typename T_prob>
    typename return_type<T_prob>::type
    binomial_lcdf(const T_n& n, const T_N& N, const T_prob& theta) {
      static const std::string function = "binomial_lcdf";
      typedef typename stan::partials_return_type<T_n, T_N, T_prob>::type
        T_partials_return;

      if (!(stan::length(n) && stan::length(N) && stan::length(theta)))
        return 0.0;

      T_partials_return P(0.0);

      check_nonnegative(function, "Population size parameter", N);
      check_finite(function, "Probability parameter", theta);
      check_bounded(function, "Probability parameter", theta, 0.0, 1.0);
      check_consistent_sizes(function,
                             "Successes variable", n,
                             "Population size parameter", N,
                             "Probability parameter", theta);

      scalar_seq_view<T_n> n_vec(n);
      scalar_seq_view<T_N> N_vec(N);
      scalar_seq_view<T_prob> theta_vec(theta);
      size_t size = max_size(n, N, theta);

      using std::exp;
      using std::pow;
      using std::log;
      using std::exp;

      operands_and_partials<T_prob> ops_partials(theta);

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

      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 theta_dbl = value_of(theta_vec[i]);
        const T_partials_return betafunc = exp(lbeta(N_dbl - n_dbl, n_dbl + 1));
        const T_partials_return Pi = inc_beta(N_dbl - n_dbl, n_dbl + 1,
                                              1 - theta_dbl);

        P += log(Pi);

        if (!is_constant_struct<T_prob>::value)
          ops_partials.edge1_.partials_[i] -= pow(theta_dbl, n_dbl)
            * pow(1 - theta_dbl, N_dbl-n_dbl - 1) / betafunc / Pi;
      }
      return ops_partials.build(P);
    }

  }
}
#endif
