Many thanks Skip for posting the reviews. Having read your post, I couldn't hold out any longer and bought the Kindle version.
Regards, Roger On May 12, 2016 8:22 AM, "Skip Cave" <[email protected]> wrote: > Below are a few reviews of John Gustafson's book "The End of Error" on > Amazon books. I've ordered a copy of the book. I wanted a hard copy, but is > back-ordered, and takes 3-4 weeks to ship. However, one can order a Kindle > electronic copy, and get it immediately. > > Also, this book answers Raul's question about worked examples. Gustafson > provides a full Mathematica implementation of Unums, so one can explore all > the ramifications of this new numerical representation. > > Skip > > <<<>>> > > "This book is revolutionary. That is the only way to describe it. I have > been a professional computer science researcher for almost 40 years, and > only once or twice before have I seen a book that is destined to make such > a profound change in the way we think about computation. It is hard to > imagine that after 70 years or so of computer arithmetic that there is > anything new to say about it, but this book reinvents the subject from the > ground up, from the very notion of finite precision numbers to their > bit-level representation, through the basic arithmetic operations, the > calculation of elementary functions, all the way to the fundamental methods > of numerical analysis, including completely new approaches to expression > calculation, root finding, and the solution of differential equations. On > every page from the beginning to the end of the book there are surprises > that just astonished me, making me re-think material that I thought had > been settled for decades. > > The methods described in this book are profoundly different from all > previous treatments of numerical methods. Unum arithmetic is an extension > of floating point arithmetic, but mathematically much cleaner. It never > does rounding, so there is no rounding error. It handles what in floating > point arithmetic is called "overflow" and "underflow" in a far more natural > and correct way that makes them normal rather than exceptional. It also > handles exceptional values (NaN, +infinity, -infinity) cleanly and > consistently. Those contributions alone would have been a profound > contribution. But the book does much more. > > One of the reasons I think the book is revolutionary is that unum-based > numerical methods can effortlessly provide provable bounds on the error in > numerical computation, something that is very rare for methods based on > floating point calculations. And the bounds are generally as tight as > possible (or as tight as you want them), rather than the useless or trivial > bounds as often happens with floating point methods or even interval > arithmetic methods. > > Another reason I consider the book revolutionary is that many of the > unum-based methods are cleanly parallelizable, even for problems that are > normally considered to be unavoidably sequential. This was completely > unexpected. > > A third reason is that in most cases unum arithmetic uses fewer bits, and > thus less power, storage, and bandwidth (the most precious resources in > today’s computers) than the comparable floating point calculation. It hard > to believe that we get this advantage in addition to all of the others, but > it is amply demonstrated in the book. Doing efficient unum arithmetic takes > more logic (e.g. transistors) than comparable floating point arithmetic > does, but as the author points out, transistors are so cheap today that > that hardly matters, especially when compared to the other benefits. > > Some of the broader themes of the book are counter > > intuitive to people like me > with > advanced conventional training, so that I have to re-think everything I > “knew” before. For example, the discussion of just what it means to “solve” > an equation numerically is extraordinarily thought provoking. Another > example is the author’s extended discussion of how calculus is not the best > inspiration for computational numerical methods, even for problems that > would seem to absolutely require calculus-based thinking, such as the > solution of ordinary differential equations. > > Not only is the content of the book brilliant, but so is the presentation. > The text is so well written, a mix of clarity, precision, and reader > friendliness that it is a pure pleasure to read, rather then the dense > struggle that mathematical textbooks usually require of the reader. But in > addition, almost every page has full color graphics and diagrams that are > completely compelling in their ability to clearly communicate the ideas. I > cannot think of any technical book I have ever seen that is so beautifully > illustrated all the way through. > > I should add that I read the Kindle edition on an iPad, and for once Amazon > did not screw up the presentation of a technical book, at least for this > platform. It is beautifully produced, in full color and detail, and with > all of the fonts and graphics reproduced perfectly. > > Dr. Gustafson has also provided a Mathematica implementation of unums and > of the many numerical methods discussed in the book. Let us hope that in > the next few years there will be implementations in other languages, > followed by hardware implementations. Over time there should be unum > arithmetic units alongside of floating point arithmetic units on every CPU > and GPU chip, and in the long run unums should replace floating point > entirely. The case the author makes for this is overwhelming. > > If you are at all interested in computer arithmetic or numerical methods, > read this book. It is destined to be a classic. > " > David Jefferson > <http://www.amazon.com/gp/pdp/profile/A3E5GY7K9GGYD0/ref=cm_cr_dp_pdp> on > April 18, 2015 > > Other > Review > s (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 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 > > Skip Cave > Cave Consulting LLC > > On Fri, Apr 29, 2016 at 12:17 PM, Skip Cave <[email protected]> > wrote: > > > Interesting comment from John Gustafson on Google Groups: > > <<<>>> > > Incidentally, I've been challenged to a debate by William Kahan at the > > ARITH23 conference, July 10-13 in San Jose, CA. (Kahn is the designer of > > the IEEE floating point numerical format). > > > > Title: "The Great Debate: The End of Error?" > > > > Kahan has apparently prepared a 34-page response to my book (Gustafson's > > "The End Of Error" book) though I have not seen it and he will probably > > spring all kinds of surprises on me. It should be a good show! > > <<<>> > > > > Skip > > On Apr 29, 2016 10:27 AM, "Skip Cave" <[email protected]> wrote: > > > > Here's the Google Group on unum computing: > > > > https://groups.google.com/forum/#!forum/unum-computing > > > > > > Here's Gustafson's home page: > > > > http://www.johngustafson.net/index.html > > > > > > Skip > > > > > > Skip Cave > > Cave Consulting LLC > > > > On Fri, Apr 29, 2016 at 5:35 AM, Pierpaolo Bernardi <[email protected] > > > > wrote: > > > >> On Fri, Apr 29, 2016 at 7:41 AM, Skip Cave <[email protected]> > >> wrote: > >> > Here's a much newer presentation by Gustafson that goes into the > >> > implementation of Unums in much more detail. > >> > > >> > > http://www.johngustafson.net/presentations/Unums2.0slides-withNotes.pdf > >> > >> This is about Unums 2.0, which is a completely different idea. The > >> choice of naming them Unums 2.0 is unfortunate IMO. > >> > >> Unums 2.0 is a way more exoteric idea then Unums, and as far as I > >> understand it is still in an embryonal stage. > >> > >> For interested people there's a google group about unums where > >> Gustafson participates, and up to now has always replied to questions. > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > >> > > > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
