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Floating-point arithmetic is by far the most widely used way of implementing real-number arithmetic on modern computers. Although the basic principles of floating-point arithmetic can be explained in a short amount of time, making such an arithmetic reliable and portable, yet fast, is a very difficult task. From the 1960s to the early 1980s, many different arithmetics were developed, but their implementation varied widely from one machine to another, making it difficult for nonexperts to design, learn, and use the required algorithms. As a result, floating-point arithmetic is far from being exploited to its full potential. 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 directly be put into practice in actual coding or design, they are illustrated, whenever possible, by a corresponding program. Key topics and features include : presentation of the history and basic concepts of floating-point arithmetic and various aspects of the past and current standards ; development of smart and nontrivial algorithms, and algorithmic possibilities induced by the availability of a fused multiply-add (fma) instruction, e.g., correctly rounded software division and square roots ; 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 : correct rounding of these functions and computation of very accurate approximations under constraints ; extensions of floating-point arithmetic such as certification, verification, and big precision.
|DATE DE PUBLICATION||2010-Jan-01|
|TAILLE DU FICHIER||5,54 MB|
|NOM DE FICHIER||Handbook of Floating-Point Arithmetic.pdf|
This handbook aims to provide a complete overview of modern floating-point arithmetic. This includes a detailed treatment of the current (IEEE-754) and next (preliminarily called IEEE-754R) standards for floating-point arithmetic.
This handbook is a definitive guide to the effective use of modern floating-point arithmetic, which has considerably evolved, from the frequently inconsistent floating-point number systems of early computing to the recent IEEE 754-2008 standard. Most of computational mathematics depends on floating-point numbers, and understanding their various implementations will allow readers to develop ...