Many properties of the IEEE-754 floating-point number system are taken for granted in
modern computers and are deeply embedded in compilers and low-level software routines …

This article presents a multiple-precision binary floating-point library, written in the ISO C
language, and based on the GNU MP library. Its particularity is to extend to arbitrary …

This book is devoted to the computation of the elementary functions. Here, we call
elementary functions the most commonly used mathematical functions: sin, cos, tan, sin− 1 …

High confidence in floating-point programs requires proving numerical properties of final
and intermediate values. One may need to guarantee that a value stays within some range …

The implementation of a correctly rounded or interval elementary function needs to be
proven carefully in the very last details. The proof requires a tight bound on the overall error …

The crlibm project aims at developing a portable, proven, correctly rounded, and efficient
mathematical library (libm) for double precision. Current libm implementation do not always …

We analyze several classical basic building blocks of double-word arithmetic (frequently
called “double-double arithmetic” in the literature): the addition of a double-word number …

This article is a case study in the implementation of a portable, proven and efficient correctly
rounded elementary function in double-precision. We describe the methodology used to …

Triple-word arithmetic consists in representing high-precision numbers as the unevaluated
sum of three floating-point numbers (with “nonoverlapping” constraints that are explicited in …

Posit is a recently proposed representation for approximating real numbers using a finite
number of bits. In contrast to the floating point (FP) representation, posit provides variable …