...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/factorials.hpp>
namespace boost{ namespace math{ template <class T> T factorial(unsigned i); template <class T, class Policy> T factorial(unsigned i, const Policy&); template <class T> T unchecked_factorial(unsigned i); template <class T> struct max_factorial; }} // namespaces
Important  

The functions described below are templates where the template argument T CANNOT be deduced from the arguments passed to the function. Therefore if you write something like:
You will get a (perhaps perplexing) compiler error, ususally indicating that there is no such function to be found. Instead you need to specify the return type explicity and write:
So that the return type is known.
Furthermore, the template argument must be a realvalued type such as
The source code
BOOST_STATIC_ASSERT(!boost::is_integral<T>::value); // factorial<unsigned int>(n) is not implemented // because it would overflow integral type T for too small n // to be useful. Use instead a floatingpoint type, // and convert to an unsigned type if essential, for example: // unsigned int nfac = static_cast<unsigned int>(factorial<double>(n)); // See factorial documentation for more detail.

template <class T> T factorial(unsigned i); template <class T, class Policy> T factorial(unsigned i, const Policy&);
Returns i!
.
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.
For i <= max_factorial<T>::value
this is implemented
by table lookup, for larger values of i
, this function
is implemented in terms of tgamma.
If i
is so large that the result can not be represented
in type T, then calls overflow_error.
template <class T> T unchecked_factorial(unsigned i);
Returns i!
.
Internally this function performs table lookup of the result. Further it
performs no range checking on the value of i: it is up to the caller to
ensure that i <= max_factorial<T>::value
. This
function is intended to be used inside inner loops that require fast table
lookup of factorials, but requires care to ensure that argument i
never grows too large.
template <class T> struct max_factorial { static const unsigned value = X; };
This traits class defines the largest value that can be passed to unchecked_factorial
.
The member value
can be
used where integral constant expressions are required: for example to define
the size of further tables that depend on the factorials.
For arguments smaller than max_factorial<T>::value
the result should be correctly rounded. For larger arguments the accuracy
will be the same as for tgamma.
Basic sanity checks and spot values to verify the data tables: the main tests for the tgamma function handle those cases already.
The factorial function is table driven for small arguments, and is implemented in terms of tgamma for larger arguments.