Every Bit Counts: Posit Computing

by John L. Gustafson

Overview

Written by one of the foremost experts in high-performance computing and the inventor of Gustafson’s law, Every Bit Counts: Posit Computing explains the foundations of a new way for computers to calculate that saves time, storage, energy, and power by packing more information into every bit than do legacy approaches. Both the AI and HPC communities are increasingly using the posit approach that Gustafson introduced in 2017, which may be the future of technical computing.

What may seem like a dry subject is made engaging by including the human and historical side of the struggle to represent numbers on machines. The book is richly illustrated in full color throughout, with every effort made to make the material as clear and accessible as possible, and even humorous.

Starting with the simplest form of the idea, the chapters gradually add concepts according to stated mathematical and engineering design principles, building a robust tool kit for creating application-specific number systems. There is also a thorough explanation of the Posit™ Standard (2022), with motivations and examples that expand on that terse 12-page document.

Product Details

ISBN-13:	9781032738055
Publisher:	CRC Press
Publication date:	11/29/2024
Series:	Chapman & Hall/CRC Computational Science
Pages:	464
Product dimensions:	7.00(w) x 10.00(h) x (d)

About the Author

Prof. John L. Gustafson is a pioneer in high-performance computing, known for a breakthrough in parallel processing (Gustafson’s law) for which he received the inaugural Gordon Bell Prize. He is a former Director at Intel Labs and a former Senior Fellow and Chief Product Architect at AMD. He now leads efforts to replace legacy computer arithmetic with high-efficiency next-generation approaches.

Table of Contents

Preface  Acknowledgements  How to Read this Book  1. The Posit Number Format  2. Inaccuracy Done Right  3. More Power!  4. How We Got Into This Mess  5. The Posit Standard, Annotated  6. Preaching About the Quire  7. A Bridge to Sane Floats  8. Logarithmic Systems, The Musical  9. The Fastest Arithmetic Ever?  10. The Minefield Method  11. Matrix Multiply, Visualized  12. Linear Solvers that Suck Less  13. The Future of Posit Computing  Glossary  Answers to Exercises  Appendix A: Posit Code Listings  Appendix B: Float Code Listings  Appendix C: The hypot Function  Appendix D: L Table for 8-Bit Posits  Appendix E: Linear Solver Tests  Appendix F: Linear Solvers  Appendix G: Takum Format  Index

Editorial Reviews

“John Gustafson is a masterful storyteller. The Every Bit Counts book takes on a seemingly dull topic – representation of numbers in computers, and makes it fascinating. Amusing at times, clear and pointed, with examples and illustrations, Gustafson critiques the state of the art and sheds light on its flaws, while showing the reader how we got here. But the real beauty of the exposé is the proposed alternative. Full of fresh ideas, new to anyone outside the ‘numbers standard’ community, the author presents a new and superior solution that revolutionizes the stagnant state of how our computers do arithmetic. Not an academic exercise, The Posit Standard is gaining acceptance in the industry. A must-read for anyone interested in how we compute for HPC and AI.”

-- David Barkai, Author of Unmatched: 50 Years of Supercomputing

“This book is a landmark work and breaks ground in the critical area of the future numerics of computing. Of greatest importance is that it finally fully exposes the gross limitations of conventional IEEE 754 floating point which reflects the ad hoc nature of its creation from its beginning to its current realization. If nothing else were to be derived from this work, burying 754 would be a major accomplishment. Gustafson’s contribution will stand for time without end or until something derived from unums and posits etc. are fully embraced and assumed by all practitioners without further thought. A critical aspect of the 13 chapters is the many areas yet to be fully explored in different regimes of application as repeatedly discussed by the author. It is pleasing to note the many credits proscribed to the many contributors over the years that have been cited by John throughout the work. This book will become required reading by the thousands of students and engineers who will derive foundational benefit for future computing methods based on this book. It makes a rare first-order contribution to the expansive nature of the field.”

-- Thomas Sterling, Ph.D, Senior Research Scientist at Texas Advanced Computing Center

“In his new book Every Bit Counts: Posit Computing, John Gustafson offers a radical re-examination of the foundations of computer arithmetic over the finite-precision real numbers. He defines an entirely new number system called posits as an alternative to traditional floating point numbers. In an expository tour-de-force he explains the many problems with floats, and then shows how posits have much better formal properties while achieving higher precision in most calculations than floats can when using the same number of bits. Pedagogically the book is brilliant. While the ideas are very sophisticated even for professional computer scientists, anyone with a college sophomore-level background in computing can grasp the key points, aided by the many beautifully rendered, colorful illustrations on almost every page. To learn about the future of computer arithmetic over real numbers, read this book. It is destined to be a classic.”

---David Jefferson, Lawrence Livermore National Laboratory (retired)

From the Publisher