MPFR

MPFR is the Multiple Precision Floating-Point Reliable Library, a C library for arbitrary-precision floating-point arithmetic with correctly rounded results. It provides a portable API for computations at any precision and is built on top of the GNU Multiple Precision Arithmetic Library (GMP), leveraging GMP’s arithmetic routines for integers and memory management.

The library is designed to guarantee correct rounding of every operation to the specified working precision. It supports multiple rounding modes, including rounding toward nearest, toward zero, toward positive infinity, and toward negative infinity. Each arithmetic or transcendental operation accepts a rounding mode parameter, and a default rounding mode can be set globally.

The core data type is mpfr_t. Initialization routines include mpfr_init and mpfr_init2 to specify precision; values can be assigned, contrasted with integers or strings, and converted to other representations. MPFR exposes a wide range of operations: basic arithmetic (add, subtract, multiply, divide), comparisons, and transcendental functions (exp, log, sin, cos, sqrt, and more), along with facilities for input/output and formatting of numbers in base representations. The API emphasizes precise control over precision and rounding, enabling reliable numerical computation across diverse applications.

Implementation and license: MPFR relies on GMP for the underlying arithmetic and memory handling. It is designed for portability across platforms and compilers, supporting common C standards. MPFR is free software distributed under the GNU Lesser General Public License (LGPL).

Use and applications: MPFR is widely used in numerical analysis, computational number theory, computer algebra systems, and formal verification, where guaranteed correct rounding and reproducible results are essential. It is commonly employed as a building block in larger mathematical libraries and research codes requiring high-precision floating-point computations.