[Beowulf] improvements on floating point arithmetic

Andrew Shewmaker agshew at gmail.com
Fri Feb 6 18:06:22 PST 2015

On Fri, Feb 6, 2015 at 11:04 AM, Andrew Shewmaker <agshew at gmail.com> wrote:

> Beowulfers,
> I was a beta reader for "The End of Error: Unum Computing" by John
> Gustafson, and I wanted to highly recommend it to everyone.
> http://www.crcpress.com/product/isbn/9781482239867
> If you want to know more about the pitfalls of floating point arithmetic,
> then you'll find it is a thorough and readable treatment. He also proposes
> a new universal number format, unum, that extends the floating point format
> with precision information and an "exact" bit.
> He's created a Mathematica reference implementation, and has used it to
> show how he can get better answers with less programmer work and moving
> fewer bits. Among its benefits, unums also provide commutativity, which
> means serial and parallel computations will give the same answer. Another
> innovation that's particularly noteworthy is support for arithmetic using
> opened and closed intervals. Unlike traditional interval arithmetic, his
> bounds don't explode.
> There's an old presentation at
> http://sites.ieee.org/scv-cs/files/2013/03/Right-SizingPrecision1.pdf ...
> I have a newer one, but didn't include it because I didn't want to spam
> everyone with a 10MB attachment.

​For those interested, that newer presentation is available at

Andrew Shewmaker
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