The End of Error: Unum Computing

by John L. Gustafson

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 Unum Computing explains a new approach to computer 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.

Genres: Technology

438 pages, Hardcover

First published January 13, 2015

Reviews

[Peter Aronson · Rating 3 out of 5]

I tend to be put off by a hard sell, and this book is a really hard sell, to the point that it reminds me of Stephen Wolfram's A New Kind of Science, and that isn't a good thing. There's a lot here to like in this book, some really interesting ideas and some wonderful presentation of those ideas, but there's a lot of comparing of apples to oranges (like a scheme with pre-computed flags compared to one without without, with no mention of the cost of pre-computing those flags). And competing systems come in for short shift; for instance, interval arithmetic as noted in this review. Even the man whom Gustafson calls "his tutor in numerical analysis", Prof. William Kahan, considered this book over broad in its claims and rather generally problematic. It does a least stop somewhat short of being an actual crank book (such as The Big Bang Never Happened: A Startling Refutation of the Dominant Theory of the Origin of the Universe or The Genealogy Of Chess).

The thing is, even though there are good and interesting ideas here, Gustafson seems to be a poor choice to put them forward because he wants to convince you of the superiority of his ideas so badly that he comes across as verging on dishonest. (Not that a moderately expense book like this and example code using a propriety system like Mathematica isn't an odd way to argue such a case in this day and age, where freely available papers and example implementations on open source platforms are more the norm.)

Gustafson appears to have done some further work on unums since this book was published, as can be seen here.

[Nick Black · Rating 5 out of 5]

haven't had my mind blown by a computer science textbook like this in years! i'm not sure i buy all the audacious claims, particularly those regarding energy savings, but every student of floating point and numerical computing ought read this novel book.