Synopsis
#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
Description
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.
Accuracy
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.
Testing
Basic sanity checks and spot values to verify the data tables: the main tests for the tgamma function handle those cases already.
Implementation
The factorial function is table driven for small arguments, and is implemented in terms of tgamma for larger arguments.