Boost Multiprecision Library

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Boost.Multiprecision is a C++ library that provides integer, rational, floating-point, complex and interval number types having more range and precision than the language's ordinary built-in types.

Language adherence:

• Boost.Multiprecision requires a compliant C++14 compiler.
• It is compatible with C++14, 17, 20, 23 and beyond.

The big number types in Boost.Multiprecision can be used with a wide selection of basic mathematical operations, elementary transcendental functions as well as the functions in Boost.Math. The Multiprecision types can also interoperate with the built-in types in C++ using clearly defined conversion rules. This allows Boost.Multiprecision to be used for all kinds of mathematical calculations involving integer, rational and floating-point types requiring extended range and precision.

Multiprecision consists of a generic interface to the mathematics of large numbers as well as a selection of big number back ends, with support for integer, rational and floating-point types. Boost.Multiprecision provides a selection of back ends delivered off-the-rack in including interfaces to GMP, MPFR, MPIR, TomMath as well as its own collection of Boost-licensed, header-only back ends for integers, rationals, floats and complex. In addition, user-defined back ends can be created and used with the interface of Multiprecision, presuming that the class implementation adheres to the necessary concepts.

Depending upon the multiprecision type, precision may be arbitrarily large (limited only by available memory), fixed at compile time (for example $50$ or $100$ decimal digits), or variable controlled at run-time by member functions. Expression templates can be enabled or disabled when configuring the number type with its backend. Most of the multiprecision types are expression-template-enabled by default. This usually provides better performance than using types configured without expression templates.

The full documentation is available on boost.org.

Using Multiprecision

In the following example, we use Multiprecision's Boost-licensed binary floating-point backend type cpp_bin_float to compute ${\sim}100$ decimal digits of

$$\sqrt{\pi} = \Gamma \left( \frac{1}{2} \right)~{\approx}~1.772453850905516027298{\ldots}\text{,}$$

where we also observe that Multiprecision can seamlesly interoperate with Boost.Math.

// ------------------------------------------------------------------------------
// Copyright Christopher Kormanyos 2024 - 2025.
// Distributed under the Boost Software License,
// Version 1.0. (See accompanying file LICENSE_1_0.txt
// or copy at http://www.boost.org/LICENSE_1_0.txt)
//

#include <boost/math/special_functions/gamma.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp>

#include <iomanip>
#include <iostream>
#include <sstream>

auto main() -> int
{
  // Configure a multiprecision binary floating-point type with approximately
  // 100 decimal digits of precision and expression templates enabled.
  // Note that the popular type cpp_bin_float_100 has already been preconfigured
  // and aliased in the multiprecision headers.

  using big_float_type = boost::multiprecision::cpp_bin_float_100;

  // In the next few lines, compute and compare sqrt(pi) with tgamma(1/2)
  // using the 100-digit multiprecision type.

  const big_float_type sqrt_pi { sqrt(boost::math::constants::pi<big_float_type>()) };

  const big_float_type half { big_float_type(1) / 2 };

  const big_float_type gamma_half { boost::math::tgamma(half) }; 

  std::stringstream strm { };

  // 1.772453850905516027298167483341145182797549456122387128213807789852911284591032181374950656738544665

  strm << std::setprecision(std::numeric_limits<big_float_type>::digits10)
       << "sqrt_pi   : "
       << sqrt_pi
       << "\ngamma_half: "
       << gamma_half;

  std::cout << strm.str() << std::endl;
}

Standalone

Defining BOOST_MP_STANDALONE allows Boost.Multiprecision to be used with the only dependency being Boost.Config. Our package on this page already includes a copy of Boost.Config. So no other downloads are required.

Some functionality is reduced in this mode. A static_assert message will alert you if a particular feature has been disabled by standalone mode. Boost.Math standalone mode is compatiable, and recommended if special functions are required for the floating point types.

Support, bugs and feature requests

Bugs and feature requests can be reported through the Gitub issue tracker (see open issues and closed issues).

You can submit your changes through a pull request.

There is no mailing-list specific to Boost Multiprecision, although you can use the general-purpose Boost mailing-list using the tag [multiprecision].

Development

Clone the whole boost project, which includes the individual Boost projects as submodules (see boost+git doc):

  git clone https://github.com/boostorg/boost
  cd boost
  git submodule update --init

The Boost.Multiprecision Library is located in libs/multiprecision/.

Running tests

First, build the b2 engine by running bootstrap.sh in the root of the boost directory. This will generate b2 configuration in project-config.jam.

  ./bootstrap.sh

Now make sure you are in libs/multiprecision/test. You can either run all the tests listed in Jamfile.v2 or run a single test:

  ../../../b2                        <- run all tests
  ../../../b2 test_complex           <- single test