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. Andrew Shewmaker
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