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. TOC:List of Figures.- List of Tables.- Preface.- Part I. Introduction, Basic Definitions, and Standards. Introduction.- Definitions and Basic Notions.- Floating-Point Formats and Environment.- Part II. Cleverly Using Floating-Point Arithmetic. Basic Properties and Algorithms.- The Fused Multiply-Add Instructions.- Enhanced Floating-Point Sums, Dot Products, and Polynomial Values.- Languages and Compilers.- Part III. Implementing Floating-Point Operators. Algorithms for the Five Basic Operations.- Hardware Implementation of Floating-Point Arithmetic.- Software Implementation of Floating-Point Arithmetic.- Part IV. Elementary Functions. Evaluating Floating-Point Elementary Functions.- Solving the Table Maker`s Dilemma.- Part V. Extensions. Formalisms for Certifying Floating-Point Algorithms.- Extending the Precision.- Part VI. Perspectives and Appendix. Conclusion and Perspectives.- Appendix: Number Theory Tools for Floating-Point Arithmetic.- Bibliography.- Index.