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How To Add Numbers

rjl on compensated summation

Gödel's Lost Letter and P=NP

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William Kahan is a numerical analyst and an expert on all things about floating point numbers. He won the 1989 Turing award for his pioneering work on how to implement floating point computations correctly. He has also been a tireless advocate for the care needed to avoid insidious numerical bugs, and his strong feelings come out in a 1997 interview for Dr. Dobbs’ Journal.

Today I want to talk about one of his results on how to sum a series of numbers.

It sounds trivial, but is really a difficult problem when inexact arithmetic is used. Since computers almost always use a fixed finite precision, the problem arises all the time, every day. Another view of adding up numbers is studied by Alexei Borodin, Persi Diaconis, and Jason Fulman in their paper on On adding a list of numbers: it is in the Bulletin of the AMS. They study…

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