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Full Description
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.
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
