# Elementary Functions: Algorithms and Implementation

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• Binding: Hardcover
• Author: Jean-Michel Muller
• Publish Date: 2016-11-17

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This textbook presents the concepts and tools necessary to understand, build, and implement algorithms for computing elementary functions (e.g., logarithms, exponentials, and the trigonometric functions). Â Both hardware- and software-oriented algorithms are included, along with issues related to accurate floating-point implementation. Â This third edition has been updated and expanded to incorporate the most recent advances in the field, new elementary function algorithms, and function software.

After a preliminary chapter that briefly introduces some fundamental concepts of computer arithmetic, such as floating-point arithmetic and redundant number systems, the text is divided into three main parts. Â Part I considers the computation of elementary functions using algorithms based on polynomial or rational approximations and using table-based methods; Â the final chapter in this section deals with basic principles of multiple-precision arithmetic. Â Part II is devoted to a presentation of âshift-and-addâ algorithms (hardware-oriented algorithms that use additions and shifts only). Â Issues related to accuracy, including range reduction, preservation of monotonicity, and correct rounding, as well as some examples of implementation are explored in Part III. Â Numerous examples of command lines and full programs are provided throughout for various software packages, including Maple, Sollya, and Gappa. Â New to this edition are an in-depth overview of the IEEE-754-2008 standard for floating-point arithmetic; a section on using double- and triple-word numbers; a presentation of new tools for designing accurate function software; and a section on the Toom-Cook family of multiplication algorithms.

The techniques presented in this book will be of interest to implementers of elementary function libraries or circuits and programmers of numerical applications. Â Additionally, graduate and advanced undergraduate students, professionals, and researchers in scientific computing, numerical analysis, software engineering, and computer engineering will find this a useful reference and resource.

PRAISE FOR PREVIOUS EDITIONS

â[T]his book seems like an essential reference for the experts (which I'm not). Â More importantly, this is an interesting book for the curious (which I am). Â In this case, you'll probably learn many interesting things from this book. Â If you teach numerical analysis or approximation theory, then this book will give you some good examples to discuss in class. â MAA Reviews (Review of Second Edition)

The rich content of ideas sketched or presented in some detail in this book is supplemented by a list of over three hundred references, most of them of 1980 or more recent. Â The book also contains some relevant typical programs. â Zentralblatt MATH (Review of Second Edition)

âI think that the book will be very valuable to students both in numerical analysis and in computer science. Â I found [it to be] well written and containing much interesting material, most of the time disseminated in specialized papers published in specialized journals difficult to find. â Numerical Algorithms (Review of First Edition)