...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

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.