Boost C++ Libraries

...one of the most highly regarded and expertly designed C++ library projects in the world. — Herb Sutter and Andrei Alexandrescu, C++ Coding Standards

Chapter 1. Boost.Multiprecision

Matthew Borland

Paul A. Bristow

Christopher Kormanyos

Janek Kozicki

John Maddock

Fahad Syed

Copyright © 2002-2025 Matthew Borland, Paul A. Bristow, Christopher Kormanyos, Janek Kozicki, John Maddock and Fahad Syed

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)

Table of Contents

Introduction

Integer Types

Factorials
Bit Operations

Floating-point Types

cpp_bin_float

cpp_dec_float

cpp_double_fp_backend

Construction from Specific Values Without Precision Loss
Area of Circle
Drop-in Caveats
Defining a Special Function.
Calculating a Derivative
Calculating an Integral
Polynomial Evaluation
Variable-Precision Newton Evaluation
Gauss-Laguerre quadrature

Interval Number Types

mpfi_float

Complex Number Types

cpp_complex
mpc_complex
complex128
complex_adaptor

Rational Number Types

cpp_rational
gmp_rational
tommath_rational
tommath_rational
rational_adaptor

Miscellaneous Number Types.

logged_adaptor
debug_adaptor
Visual C++ Debugger Visualizers

Forward Declarations

Constructing and Interconverting Between Number Types

Generating Random Numbers

Primality Testing

Literal Types and constexpr Support

Importing and Exporting Data to and from cpp_int and cpp_bin_float

Rounding Rules for Conversions

Mixed Precision Arithmetic

Variable Precision Arithmetic

Generic Integer Operations

Boost.Serialization Support

Numeric Limits

std::numeric_limits<> constants
std::numeric_limits<> functions
Numeric limits for 32-bit platform
How to Determine the Kind of a Number From std::numeric_limits

Input Output

Hash Function Support

Eigen Interoperability

Writing a New Backend

number
cpp_int
gmp_int
tom_int
gmp_float
mpfr_float_backend
cpp_bin_float
cpp_dec_float
cpp_double_fp_backend
Internal Support Code
Backend Requirements
Header File Structure

Performance Comparison

The Overhead in the Number Class Wrapper
Floating-Point Real World Tests
Integer Real World Tests
Rational Real World Tests
Float Algorithm Performance
Integer Algorithm Performance
Rational Type Performance

History
TODO
FAQ
Acknowledgements

Function Index
Class Index
Typedef Index
Index