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Full Description
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.
Contents
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.
