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

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

The special functions and tools in this library can be used with MPFR (an arbitrary precision number type based on the GNU Multiple Precision Arithmetic Library), either via the bindings in boost/math/bindings/mpfr.hpp, or via boost/math/bindings/mpreal.hpp.

**New projects are recommended to use Boost.Multiprecision
with GMP/MPFR backend instead.**

In order to use these bindings you will need to have installed MPFR plus its dependency the GMP library. You will also need one of the two supported C++ wrappers for MPFR: gmpfrxx (or mpfr_class), or mpfr-C++ (mpreal).

Unfortunately neither `mpfr_class`

nor `mpreal`

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
and boost/math/bindings/mpreal.hpp
that you should use in place of including 'gmpfrxx.h' or 'mpreal.h' directly.
The classes `mpfr_class`

or
`mpreal`

are then usable unchanged
once this header is included, so for example `mpfr_class`

'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; }

Alternatively use with `mpreal`

would look like:

#include <boost/math/bindings/mpreal.hpp> #include <boost/math/special_functions/gamma.hpp> int main() { mpfr::mpreal::set_precision(500); // 500 bit precision mpfr::mpreal v = boost::math::tgamma(sqrt(mpfr::mpreal(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 either `mpfr_class`

or `mpreal`

.

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