Stan Math Library  2.15.0
reverse mode automatic differentiation
binomial_coefficient_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_FUN_BINOMIAL_COEFFICIENT_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_FUN_BINOMIAL_COEFFICIENT_LOG_HPP
3 
4 #include <boost/math/special_functions/gamma.hpp>
5 #include <boost/math/tools/promotion.hpp>
6 
7 namespace stan {
8  namespace math {
59  template <typename T_N, typename T_n>
60  inline typename boost::math::tools::promote_args<T_N, T_n>::type
61  binomial_coefficient_log(const T_N N, const T_n n) {
62  using std::log;
63  using boost::math::lgamma;
64  const double CUTOFF = 1000;
65  if (N - n < CUTOFF) {
66  T_N N_plus_1 = N + 1;
67  return lgamma(N_plus_1) - lgamma(n + 1) - lgamma(N_plus_1 - n);
68  } else {
69  typename boost::math::tools::promote_args<T_N, T_n>::type N_minus_n
70  = N - n;
71  double one_twelfth = 1.0 / 12;
72  return n * log(N_minus_n)
73  + (N + 0.5) * log(N / N_minus_n)
74  + one_twelfth / N
75  - n
76  - one_twelfth / N_minus_n
77  - lgamma(n + 1);
78  }
79  }
80 
81  }
82 }
83 #endif
fvar< T > binomial_coefficient_log(const fvar< T > &x1, const fvar< T > &x2)
fvar< T > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
Definition: lgamma.hpp:20
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14

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