binomial_coefficient_log.hpp

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#ifndef STAN__MATH__FUNCTIONS__BINOMIAL_COEFFICIENT_LOG_HPP
#define STAN__MATH__FUNCTIONS__BINOMIAL_COEFFICIENT_LOG_HPP

#include <boost/math/special_functions/gamma.hpp>
#include <boost/math/tools/promotion.hpp>

namespace stan {

  namespace math {

    template <typename T_N, typename T_n>
    inline typename boost::math::tools::promote_args<T_N, T_n>::type
    binomial_coefficient_log(const T_N N, const T_n n) {
      using std::log;
      using boost::math::lgamma;

      const double cutoff = 1000;
      if ((N < cutoff) || (N - n < cutoff)) {
        return lgamma(N + 1.0) - lgamma(n + 1.0) - lgamma(N - n + 1.0);
      } else {
        return n * log(N - n) + (N + 0.5) * log(N/(N-n))
          + 1/(12*N) - n - 1/(12*(N-n)) - lgamma(n + 1.0);
      }
    }

  }
}

#endif