On Saturday, 11 July 2015 at 03:02:24 UTC, Nick B wrote:
On Thursday, 20 February 2014 at 10:10:13 UTC, Nick B wrote:
Hi everyone.
John Gustafson Will be presenting a Keynote on Thursday 27th
February at 11:00 am
The abstract is here:
http://openparallel.com/multicore-world-2014/speakers/john-gustafson/
There is also a excellent background paper, (PDF - 64 pages)
which can be found here:
FYI
John Gustafson book is now out:
It can be found here:
http://www.amazon.com/End-Error-Computing-Chapman-Computational/dp/1482239868/ref=sr_1_1?s=books&ie=UTF8&qid=1436582956&sr=1-1&keywords=John+Gustafson&pebp=1436583212284&perid=093TDC82KFP9Y4S5PXPY
Here is one of the reviewers comments:
9 of 9 people found the following review helpful
This book is revolutionary
By David Jefferson on April 18, 2015
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 counterintuitive to
people like me 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.
To be honest, that sound like snake oil salesman speech to me
rather than science. It's all hand waving and nothing concrete is
provided, the whole thing wrapped in way too much superlatives.
The guy seems to have good credential. Why should I read that
book ?
