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

Clune, Thomas L. GSFC-6101 thomas.l.clune
Mon Aug 14 17:06:44 EDT 2017

I agree with many of the points that Kahan made, but it seems to me that he?s overstating some of the concerns just a bit.      The book was written for a less technical audience and was unabashedly selling something.

My biggest technical objection was that the coffin approach does not scale very well to 100 dimensions.   Sampling among 2^100 boxes for a 100 species chemical solver might scale well if I had a google (the number, not the company) of processs, but it will take forever to run on a billion cores.  :-)

On Aug 14, 2017, at 4:24 PM, Keith Bierman <khbkhb at gmail.com<mailto:khbkhb at gmail.com>> wrote:

Kahan's argument boils down to "it's misleading and the results can't be trusted" in which case the difficulty in adoption isn't really relevant ;>

I know and like Gus and Velvel ... I'd like Gus to be right; but I fear Velvel is.

Keith Bierman
khbkhb at gmail.com<mailto:khbkhb at gmail.com>
303 997 2749

On Mon, Aug 14, 2017 at 2:22 PM, Clune, Thomas L. (GSFC-6101) <thomas.l.clune at nasa.gov<mailto:thomas.l.clune at nasa.gov>> wrote:
I read this book and greatly enjoyed it.    I don?t think there is a realistic path for adoption, but it was enlightening.


> On Aug 14, 2017, at 2:38 PM, Van Snyder <Van.Snyder at jpl.nasa.gov<mailto:Van.Snyder at jpl.nasa.gov>> wrote:
> Beating floating point at its own game
> https://insidehpc.com/2017/08/beating-floating-point-game-posit-arithmetic/
> Editorial reviews from Amazon:
> https://www.amazon.com/End-Error-Computing-Chapman-Computational/dp/1482239868/ref=sr_1_1?s=books&ie=UTF8&qid=1413144875&sr=1-1&keywords=end+of+error+gustafson
> "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
> follow."
> ?Jack Dongarra, University Distinguished Professor, University of
> Tennessee
> "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
> adoption."
> ?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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