New Approach Could Sink Floating Point Computation

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THE END of ERROR
Unum Computing
John L. Gustafson

CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2015 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business

Preface
“The purpose of mathematics is to eliminate thought.” —Philip G. Saffman (1931 – 2008)
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Formulas, numbers, and computer code all make a book harder to read. The densest code is relegated to the appendices to relieve this, and in general the reader does not need to read the code sections to understand what follows. This book was written in Mathematica, a good way to make sure the math is sound and the graphs are correct. In one example, a four-bit “unum” value gets the right answer whereas a quadruple precision (128-bit) float fails; the main reason the code is shown is because some skeptics would otherwise not believe such calculations are possible, and would suspect smoke-and-mirrors. Everything needed to define a complete, working, rigorous computing environment is here.
None of the new ideas presented here are patented or pending patents, and that is quite intentional.
The purpose of the unum approach is to eliminate thought.
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Acknowledgments
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What kind of nut cares this much about computer arithmetic? I have had the honor and pleasure of working with and meeting several members of the equally obsessed.
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I save my deepest appreciation for last. In 2012, I visited a legendary Berkeley professor named William Kahan just after discovering the ubox method. We spent six hours talking about everything from the IEEE Standard to n-body dynamics to car repair. The cool thing about the visit is that I got to thank him for introducing me to numerical analysis. You see, Professor Kahan was the man who created the software for the HP calculators that introduced me to the hazards of rounding error. He has therefore been my tutor in numerical analysis, one way or another, for almost forty years. {emphasis mine}

Thank you, Professor Kahan.

BEST!
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my apologies to all: the above narrative is an extract from the aforementioned publication. I should have clearly stated this upfront.