#ifndef STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_LCCDF_HPP
#define STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_LCCDF_HPP

#include <boost/random/gamma_distribution.hpp>
#include <boost/random/variate_generator.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_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/err/check_not_nan.hpp>
#include <stan/math/prim/scal/err/check_positive_finite.hpp>
#include <stan/math/prim/scal/fun/size_zero.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <stan/math/prim/scal/fun/lgamma.hpp>
#include <stan/math/prim/scal/fun/gamma_p.hpp>
#include <stan/math/prim/scal/fun/digamma.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/scalar_seq_view.hpp>
#include <stan/math/prim/scal/meta/VectorBuilder.hpp>
#include <stan/math/prim/scal/meta/partials_return_type.hpp>
#include <stan/math/prim/scal/meta/return_type.hpp>
#include <stan/math/prim/scal/fun/grad_reg_inc_gamma.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <cmath>
#include <limits>

namespace stan {
namespace math {

template <typename T_y, typename T_shape, typename T_scale>
typename return_type<T_y, T_shape, T_scale>::type inv_gamma_lccdf(
    const T_y& y, const T_shape& alpha, const T_scale& beta) {
  typedef typename stan::partials_return_type<T_y, T_shape, T_scale>::type
      T_partials_return;

  if (size_zero(y, alpha, beta))
    return 0.0;

  static const char* function = "inv_gamma_lccdf";

  using boost::math::tools::promote_args;
  using std::exp;

  T_partials_return P(0.0);

  check_positive_finite(function, "Shape parameter", alpha);
  check_positive_finite(function, "Scale parameter", beta);
  check_not_nan(function, "Random variable", y);
  check_nonnegative(function, "Random variable", y);
  check_consistent_sizes(function, "Random variable", y, "Shape parameter",
                         alpha, "Scale Parameter", beta);

  scalar_seq_view<T_y> y_vec(y);
  scalar_seq_view<T_shape> alpha_vec(alpha);
  scalar_seq_view<T_scale> beta_vec(beta);
  size_t N = max_size(y, alpha, beta);

  operands_and_partials<T_y, T_shape, T_scale> ops_partials(y, 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(y); i++) {
    if (value_of(y_vec[i]) == 0)
      return ops_partials.build(0.0);
  }

  using boost::math::tgamma;
  using std::exp;
  using std::log;
  using std::pow;

  VectorBuilder<!is_constant_struct<T_shape>::value, T_partials_return, T_shape>
      gamma_vec(stan::length(alpha));
  VectorBuilder<!is_constant_struct<T_shape>::value, T_partials_return, T_shape>
      digamma_vec(stan::length(alpha));

  if (!is_constant_struct<T_shape>::value) {
    for (size_t i = 0; i < stan::length(alpha); i++) {
      const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
      gamma_vec[i] = tgamma(alpha_dbl);
      digamma_vec[i] = digamma(alpha_dbl);
    }
  }

  for (size_t n = 0; n < N; n++) {
    // Explicit results for extreme values
    // The gradients are technically ill-defined, but treated as zero
    if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
      return ops_partials.build(negative_infinity());

    const T_partials_return y_dbl = value_of(y_vec[n]);
    const T_partials_return y_inv_dbl = 1.0 / y_dbl;
    const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
    const T_partials_return beta_dbl = value_of(beta_vec[n]);

    const T_partials_return Pn = gamma_p(alpha_dbl, beta_dbl * y_inv_dbl);

    P += log(Pn);

    if (!is_constant_struct<T_y>::value)
      ops_partials.edge1_.partials_[n]
          -= beta_dbl * y_inv_dbl * y_inv_dbl * exp(-beta_dbl * y_inv_dbl)
             * pow(beta_dbl * y_inv_dbl, alpha_dbl - 1) / tgamma(alpha_dbl)
             / Pn;
    if (!is_constant_struct<T_shape>::value)
      ops_partials.edge2_.partials_[n]
          -= grad_reg_inc_gamma(alpha_dbl, beta_dbl * y_inv_dbl, gamma_vec[n],
                                digamma_vec[n])
             / Pn;
    if (!is_constant_struct<T_scale>::value)
      ops_partials.edge3_.partials_[n]
          += y_inv_dbl * exp(-beta_dbl * y_inv_dbl)
             * pow(beta_dbl * y_inv_dbl, alpha_dbl - 1) / tgamma(alpha_dbl)
             / Pn;
  }
  return ops_partials.build(P);
}

}  // namespace math
}  // namespace stan
#endif
