Great Roger! I'll be interested to see what you think about the book, and Gustafson's proposed new binary number format. I haven't received my hard copy of his book as yet. On May 12, 2016 11:28 AM, "roger stokes" <[email protected]> wrote:
> 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
