ABSTRACT

The Future of Numerical Computing

Written by one of the foremost experts in high-performance computing and the inventor of Gustafson’s Law, The End of Error: Unum Computing explains a new approach to computer arithmetic: the universal number (unum). The unum encompasses all IEEE floating-point formats as well as fixed-point and exact integer arithmetic. This new number type obtains more accurate answers than floating-point arithmetic yet uses fewer bits in many cases, saving memory, bandwidth, energy, and power.

A Complete Revamp of Computer Arithmetic from the Ground Up

Richly illustrated in color, this groundbreaking book represents a fundamental change in how to perform calculations automatically. It illustrates how this novel approach can solve problems that have vexed engineers and scientists for decades, including problems that have been historically limited to serial processing.

Suitable for Anyone Using Computers for Calculations

The book is accessible to anyone who uses computers for technical calculations, with much of the book only requiring high school math. The author makes the mathematics interesting through numerous analogies. He clearly defines jargon and uses color-coded boxes for mathematical formulas, computer code, important descriptions, and exercises.

chapter 2|18 pages

Building up to the unum format

chapter 4|20 pages

The complete unum format

chapter 5|30 pages

Hidden scratchpads and the three layers

chapter 6|8 pages

Information per bit

chapter 7|10 pages

Fixed-size unum storage

chapter 8|8 pages

Comparison operations

chapter 10|14 pages

Multiplication and division

chapter 11|14 pages

Powers

chapter 12|4 pages

Other important unary operations

chapter 13|14 pages

Fused operations (single-use expressions)

chapter |2 pages

Part 1 Summary

chapter 16|18 pages

Avoiding interval arithmetic pitfalls

chapter 18|16 pages

Permission to guess

chapter 19|14 pages

Pendulums done correctly

chapter 20|24 pages

The two-body problem (and beyond)

chapter 21|16 pages

Calculus considered evil: Discrete physics

chapter 22|6 pages

The end of error

chapter |4 pages

Glossary

chapter |6 pages

Appendix A: Glossary of unum functions

chapter |4 pages

Appendix B: Glossary of ubox functions

chapter |36 pages

Appendix C: Algorithm listings for Part 1

chapter |18 pages

Appendix D: Algorithm listings for Part 2

chapter |2 pages

For Further Reading