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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
9 namespace math {
10
61 template <typename T_N, typename T_n>
62 inline typename boost::math::tools::promote_args<T_N, T_n>::type
63 binomial_coefficient_log(const T_N N, const T_n n) {
64 using std::log;
65 using boost::math::lgamma;
66
67 const double cutoff = 1000;
68 if ((N < cutoff) || (N - n < cutoff)) {
69 return lgamma(N + 1.0) - lgamma(n + 1.0) - lgamma(N - n + 1.0);
70 } else {
71 return n * log(N - n) + (N + 0.5) * log(N/(N-n))
72 + 1/(12*N) - n - 1/(12*(N-n)) - lgamma(n + 1.0);
73 }
74 }
75
76 }
77 }
78
79 #endif
stan::math::binomial_coefficient_log
fvar< T > binomial_coefficient_log(const fvar< T > &x1, const fvar< T > &x2)
Definition: binomial_coefficient_log.hpp:16
stan::math::lgamma
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:15
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15

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