Handbook of Floating-Point Arithmetic

This handbook aims to provide a complete overview of modern floating-point arithmetic, including a detailed treatment of the newly revised (IEEE 754-2008) standard for floating-point arithmetic. Presented throughout are algorithms for implementing floating-point arithmetic as well as algorithms that use floating-point arithmetic. So that the techniques presented can be put directly into practice in actual coding or design, they are illustrated, whenever possible, by a corresponding program.Key topics and features include a presentation of the history and basic concepts of floating-point arithmetic; a development of smart and nontrivial algorithms, and algorithmic possibilities induced by the availability of a fused multiply-add (fma) instruction; implementation of floating-point arithmetic either in software—on an integer processor—or hardware, and a discussion of issues related to compilers and languages; coverage of several recent advances related to elementary functions; and extensions of floating-point arithmetic such as certification, verification, and precision.Handbook of Floating-Point Arithmetic is designed for programmers of numerical applications, compiler designers, programmers of floating-point algorithms, designers of arithmetic operators, and more generally, students and researchers in numerical analysis who wish to better understand a tool used in their daily work and research.