到目前为止，浮点算法是现代计算机上实现实数算法最广泛使用的方法。虽然浮点运算的基本原理可以在很短的时间内解释，但要使这种算法可靠、可移植且快速，是一项非常困难的任务。从20世纪60年代到80年代初，人们开发了许多不同的算法，但它们的实现在不同的机器之间差异很大，这使得非专家很难设计、学习和使用所需的算法。因此，浮点运算远未充分发挥其潜力。
本手册旨在全面概述现代浮点运算，包括对最新修订的（IEEE 754-2008）浮点运算标准的详细介绍。自始至终都介绍了实现浮点算法的算法以及使用浮点算法的算法。为了使所介绍的技术能够直接应用于实际的编码或设计中，只要有可能，就会用相应的程序对其进行说明。
主要主题和功能包括
*介绍浮点运算的历史和基本概念，以及过去和当前标准的各个方面
*智能和非平凡算法的开发，以及由融合乘法-加法（fma）指令的可用性引起的算法可能性，例如，正确四舍五入的软件除法和平方根
*浮点算法的实现，无论是在整数处理器的软件中还是在硬件中，以及与编译器和语言有关的问题的讨论
*涵盖与初等函数有关的几个最新进展：这些函数的正确舍入和约束下非常精确的近似计算
*浮点算法的扩展，如认证、验证和大精度
《浮点算术手册》是为数值应用程序员、编译器设计师、浮点算法程序员、算术运算符设计师，以及更广泛地为希望更好地理解日常工作和研究中使用的工具的数值分析学生和研究人员而设计的。
Handbook of Floating-Point Arithmetic, First Edition
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 be put directly 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
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.
OR
