...one of the most highly
regarded and expertly designed C++ library projects in the
world.

— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards

#include <boost/math/special_functions/binomial.hpp>

namespace boost{ namespace math{ template <class T> T binomial_coefficient(unsigned n, unsigned k); template <class T, class Policy> T binomial_coefficient(unsigned n, unsigned k, const Policy&); }} // namespaces

Returns the binomial coefficient: _{n}C_{k}.

Requires k <= n.

The final Policy argument is optional and can be used to control the behaviour of the function: how it handles errors, what level of precision to use etc. Refer to the policy documentation for more details.

May return the result of overflow_error if the result is too large to represent in type T.

Important | |
---|---|

The functions described above are templates where the template argument T can not be deduced from the arguments passed to the function. Therefore if you write something like:
You will get a compiler error, ususally indicating that there is no such function to be found. Instead you need to specifiy the return type explicity and write:
So that the return type is known. Further, the template argument must
be a real-valued type such as |

The accuracy will be the same as for the factorials for small arguments (i.e. no more than one or two epsilon), and the beta function for larger arguments.

The spot tests for the binomial coefficients use data generated by functions.wolfram.com.

Binomial coefficients are calculated using table lookup of factorials where possible using:

_{n}C_{k} = n! / (k!(n-k)!)

Otherwise it is implemented in terms of the beta function using the relations:

_{n}C_{k} = 1 / (k * beta(k,
n-k+1))

and

_{n}C_{k} = 1 / ((n-k) * beta(k+1,
n-k))