The End of Error

Written by one of the foremost experts in high-performance computing and the inventor of Gustafson's Law, this groundbreaking book 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. Richly illustrated in color, the book is accessible to anyone who uses computers for technical calculations.

Dr. John L. Gustafson is an applied physicist and mathematician. He is a former Director at Intel Labs and former Chief Product Architect at AMD. A pioneer in high-performance computing, he introduced cluster computing in 1985 and first demonstrated scalable massively parallel performance on real applications in 1988. This became known as Gustafson's Law, for which he won the inaugural ACM Gordon Bell Prize. He is also a recipient of the IEEE Computer Society's Golden Core Award. Find more details on his website.

Part 1 A New Number Format: The Unum: Overview. Building up to the unum format. The "original sin" of computer arithmetic. The complete unum format. Hidden scratchpads and the three layers. Information per bit. Fixed-size unum storage. Comparison operations. Add/subtract, and the unbiased rounding myth. Multiplication and division. Powers. Other important unary operations. Fused operations (single-use expressions). Trial runs: Unums face challenge calculations. Part 2 A New Way to Solve: The Ubox: The other kind of error. Avoiding interval arithmetic pitfalls. What does it mean to "solve" an equation? Permission to guess. Pendulums done correctly. The two-body problem (and beyond). Calculus considered evil: Discrete physics. The end of error. Glossary. For further reading. Appendices. Index.