(j3.2006) [Fwd: Beating floating point at its own game]

Van Snyder Van.Snyder
Mon Aug 14 14:38:29 EDT 2017

Beating floating point at its own game


Editorial reviews from Amazon:

"The author of the present book believes that it is time to supplement
the century-old floating point arithmetic with something better: unum
arithmetic. The book covers various operations with unum arithmetic and
topics like polynomial evaluation, solving equations, two-body problem,
etc. The appendices give a glossary of unum functions, ubox functions,
and some algorithm listings."
?Zentralblatt MATH 1320

"This book is an extraordinary reinvention of computer arithmetic and
elementary numerical methods from the ground up. Unum arithmetic is an
extension of floating point in which it is also possible to represent
the open intervals between two floating point numbers. This leads to
arithmetic that is algebraically much cleaner, without rounding error,
overflow underflow, or negative zero, and with clean and consistent
treatment of positive and negative infinity and NaN. These changes are
not just marginal technical improvements. As the book fully
demonstrates, they lead to what can only be described as a radical
re-foundation of elementary numerical analysis, with new methods that
are free of rounding error, fully parallelizable, fully portable, easier
for programmers to master, and often more economical of memory,
bandwidth, and power than comparable floating point methods. The book is
exceptionally well written and produced and is illustrated on every page
with full-color diagrams that perfectly communicate the material. Anyone
interested in computer arithmetic or numerical methods must read this
book. It is surely destined to be a classic."
?David Jefferson, Center for Advanced Scientific Computing, Lawrence
Livermore National Laboratory

"John Gustafson?s book The End of Error presents the ideas of computer
arithmetic in a very easy-to-read and understandable form. While the
title is provocative, the content provides an illuminating discussion of
the issues. The examples are engaging, well thought out, and simple to
?Jack Dongarra, University Distinguished Professor, University of

"John Gustafson presents a bold and brilliant proposal for a
revolutionary number representation system, unum, for scientific (and
potentially all other) computers. Unum?s main advantage is that
computing with these numbers gives scientists the correct answer all the
time. Gustafson is able to show that the universal number, or unum,
encompasses all standard floating-point formats as well as fixed-point
and exact integer arithmetic. The book is a call to action for the next
stage: implementation and testing that would lead to wide-scale
?Gordon Bell, Researcher Emeritus, Microsoft Research

"Reading more and more in [John Gustafson?s] book became a big surprise.
I had not expected such an elaborate and sound piece of work. It is hard
to believe that a single person could develop so many nice ideas and put
them together into a sketch of what perhaps might be the future of
computing. Reading [this] book is fascinating."
?Ulrich Kulisch, Karlsruhe Institute of Technology, Germany

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