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Handbook of floating-point arithmetic. 2nd edition. (English) Zbl 1394.65001
Cham: Birkhäuser (ISBN 978-3-319-76525-9/hbk; 978-3-319-76526-6/ebook). xxv, 627 p. (2018).
The new edition of this book updates chapters to reflect recent changes to programming languages and compilers and the new prevalence of Graphic Processing Units in recent years. The revision also add material on fused multiply-add instruction and methods of extending the floating point precision
The first part of the book presents the history and basic concepts of floating-point arithmetic (formats, exceptions, correct rounding, etc.) and various aspects of the 2008 version of the IEEE 754 standard. The second part shows how the features of the standard can be used to develop effective and nontrivial algorithms. This includes summation algorithms, and division and square root relying on a fused multiply-add. This part also discusses issues related to compilers and languages. The third part then explains how to implement floating-point arithmetic, both in software (on an integer processor) and in hardware (VLSI or reconfigurable circuits). It also surveys the implementation of elementary functions. The fourth part presents some extensions: complex numbers, interval arithmetic, verification of floating-point arithmetic, and extension of the precision. In the Appendix, the reader will find an introduction to relevant number theory tools and a brief presentationnof the standards that predated IEEE 754-2008. This book is designed for programmers of numerical applications, compiler designers, programmers of floating-point algorithms, designers of arithmetic operators (floating point adders, multipliers, dividers, . . . ), and more generally students and researchers in numerical analysis who wish to more accurately understand a tool that they manipulate on an everyday basis.

MSC:
65-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to numerical analysis
68-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to computer science
65Y04 Numerical algorithms for computer arithmetic, etc.
65G50 Roundoff error
68M07 Mathematical problems of computer architecture
68N15 Theory of programming languages
68N20 Theory of compilers and interpreters
68W35 Hardware implementations of nonnumerical algorithms (VLSI algorithms, etc.)
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