This book constitutes the refereed proceedings of the Third International Congress on Mathematical Software, ICMS 2010, held in Kobe, Japan in September 2010. The 49 revised full papers presented were carefully reviewed and selected for presentation. The papers are organized in topical sections on computational group theory, computation of special functions, computer algebra and reliable computing, computer tools for mathematical editing and scientific visualization, exact numeric computation for algebraic and geometric computation, formal proof, geometry and visualization, Groebner bases and applications, number theoretical software as well as software for optimization and polyhedral computation.

This book constitutes the proceedings of the 5th International Conference on Mathematical Software, ICMS 2015, held in Berlin, Germany, in July 2016. The 68 papers included in this volume were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections named: univalent foundations and proof assistants; software for mathematical reasoning and applications; algebraic and toric geometry; algebraic geometry in applications; software of polynomial systems; software for numerically solving polynomial systems; high-precision arithmetic, effective analysis, and special functions; mathematical optimization; interactive operation to scientific artwork and mathematical reasoning; information services for mathematics: software, services, models, and data; semDML: towards a semantic layer of a world digital mathematical library; miscellanea.

This book constitutes the proceedings of the 4th International Conference on Mathematical Software, ICMS 2014, held in Seoul, South Korea, in August 2014. The 108 papers included in this volume were carefully reviewed and selected from 150 submissions. The papers are organized in topical sections named: invited; exploration; group; coding; topology; algebraic; geometry; surfaces; reasoning; special; Groebner; triangular; parametric; interfaces and general.

The ICMS Developer's Meeting is an international congress for which the main theme is mathematical software. The 2010 meeting was the third of a series of meetings of similar theme, the ?rst being held in Beijing, China in 2002,and the second in Castro-Urdiales, Spain in 2006. The ?eld of mathematics has numerous branches, and in each branch we ?nd that algorithms, and also implementations and applications of software s- tems, are studied. Researchers who endeavor to make such studies also have international meetings within their speci'c branches of mathematics, and these meetings have made signi'cant contributions to the ?elds in which they lie. The ICMS (International Congresseson Mathematical Software), on the other hand, is a general (not branch speci'c) meeting on mathematical software, which is held every four years, and is a rare opportunity for developers of mathematical softwarefrom di'erent branchesof mathematics, as well as mathematicians who are interested in mathematical software, to gather together.

This book constitutes the proceedings of the 6th International Conference on Mathematical Software, ICMS 2018, held in South Bend, IN, USA, in July 2018.The 59 papers included in this volume were carefully reviewed and selected from numerous submissions. The program of the 2018 meeting consisted of 20 topical sessions, each of which providing an overview of the challenges, achievements and progress in a subeld of mathematical software research, development and use.

This book constitutes the proceedings of the 7th International Conference on Mathematical Software, ICMS 2020, held in Braunschweig, Germany, in July 2020. The 48 papers included in this volume were carefully reviewed and selected from 58 submissions. The program of the 2020 meeting consisted of 20 topical sessions, each of which providing an overview of the challenges, achievements and progress in a environment of mathematical software research, development and use.

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). Both hardware- and software-oriented algorithms are included, along with issues related to accurate floating-point implementation. 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. Part I considers the computation of elementary functions using algorithms based on polynomial or rational approximations and using table-based methods; the final chapter in this section deals with basic principles of multiple-precision arithmetic. Part II is devoted to a presentation of “shift-and-add” algorithms (hardware-oriented algorithms that use additions and shifts only). 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. Numerous examples of command lines and full programs are provided throughout for various software packages, including Maple, Sollya, and Gappa. 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. 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 “[T]his book seems like an essential reference for the experts (which I'm not). More importantly, this is an interesting book for the curious (which I am). In this case, you'll probably learn many interesting things from this book. If you teach numerical analysis or approximation theory, then this book will give you some good examples to discuss in class." — 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. The book also contains some relevant typical programs." — Zentralblatt MATH (Review of Second Edition) “I think that the book will be very valuable to students both in numerical analysis and in computer science. 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." — Numerical Algorithms (Review of First Edition)