Boost C++ Libraries

The special functions and tools in this library can be used with MPFR (an arbitrary precision number type based on the GMP library), via the bindings in boost/math/bindings/mpfr.hpp.

In order to use these binings you will need to have installed MPFR plus it's dependency the GMP library and the C++ wrapper for MPFR known as gmpfrxx (or mpfr_class).

Unfortunately mpfr_class doesn't quite satisfy our conceptual requirements, so there is a very thin set of additional interfaces and some helper traits defined in boost/math/bindings/mpfr.hpp that you should use in place of including 'gmpfrxx.h' directly. The existing mpfr_class is then usable unchanged once this header is included, so it's performance-enhancing expression templates are preserved and fully supported by this library:

#include <boost/math/bindings/mpfr.hpp>
#include <boost/math/special_functions/gamma.hpp>

int main()
{
   mpfr_class::set_dprec(500); // 500 bit precision
   //
   // Note that the argument to tgamma is an expression template,
   // that's just fine here:
   //
   mpfr_class v = boost::math::tgamma(sqrt(mpfr_class(2)));
   std::cout << std::setprecision(50) << v << std::endl;
}

For those functions that are based upon the Lanczos approximation, the bindings defines a series of approximations with up to 61 terms and accuracy up to approximately 3e-113. This therefore sets the upper limit for accuracy to the majority of functions defined this library when used with mpfr_class.

There is a concept checking test program for mpfr support here.