Compiled by G. W. Stewart, firstname.lastname@example.org On October 11,
1999, I posted the following query in
the NA Digest.
giving a talk later this month on rounding error to the Baltimore-Washington
Section of SIAM. I would appreciate any
interesting anecdotes on real-life embarrassments due to rounding error. I
recall (though I don't know the details) stories about an index on the
Canadian stock market drifting off true and something about a missile in the
Iraq war. If you know the details of these or any other stories, please pass
them on to me.
The response was
certainly gratifying. Within two days I received 64 messages. They were a
great help in preparing my talk, which I gave on October 20 at Johns Hopkins.
My thanks to everyone. (For those who are interested, a postscript file of my
transparencies can be found at ftp://thales.cs.umd.edu/pub/misc/roundtalk.ps)
I was surprised to find
how few incidents were reported. Apparently, with some notable exceptions,
the problems due to roundoff are themselves at the
level of roundoff.
Many responders asked
me to post a summary. Here is a list of the incidents I used in my talk with
references and a brief description.
1. The Patriot and the
- General Accounting Office
- Robert Skeel,
"Roundoff Error Cripples Patriot Missile,"
SIAM News, July 1992.
On February 25, 1991, during the Gulf War, a Patriot missile defense system
let a Scud get through. It hit a barracks, killing 28 people. The problem was
in the differencing of floating point numbers obtained by converting and scaling
an integer timing register. The GAO report has less than the full story. For
that see Skeel's excellent article.
2. The short flight of
the Ariane 5.
- 1. Report by the Inquiry
the first Ariane 5 was launched. All went well for
36 seconds. Then the Ariane veered off course and
self-destructed. The problem was in the Inertial Reference System, which
produced an operation exception trying to convert a 64-bit floating-point
number to a 12-bit integer. It sent a diagnostic word to the On-Board
Computer, which interpreted it as flight data. Finis.
computation was done by legacy software from the Ariane
4, and its results were not needed after lift-off.
3. The Vancouver Stock Exchange
(References communicated by Valerie Fraysse)
- The Wall Street Journal November 8, 1983, p.37.
- The Toronto Star, November 19, 1983.
- B.D. McCullough and H.D. Vinod, Journal of Economic Literature, Vol XXXVII (June 1999), pp. 633-665.
(I figure) the Vancouver Stock Exchange instituted a new index initialized to
a value of 1000.000. The index was updated after each transaction. Twenty two
months later it had fallen to 520. The cause was that the updated value was
truncated rather than rounded. The rounded calculation gave a value of
elections in Schleswig-Holstein.
- Rounding error changes
Parliament makeup, Debora Weber-Wulff, The
Risks Digest, Volume 13, Issue 37, 1992. catless.ncl.ac.uk/Risks
German parliamentary elections, a party with less than 5.0% of the vote
cannot be seated. The Greens appeared to have a cliff-hanging 5.0%, until it
was discovered (after the results had been announced) that they really had
only 4.97%. The printout was to two figures, and the actual percentage was
rounded to 5.0%.
5. More examples
few more examples try searching the RISK Digest (catless.ncl.ac.uk/Risks) with the
key word "rounding" (David Goldberg's idea).
1995-2001 Dr. George F. Corliss, Marquette University, EECE/MSCS -- All rights reserved.
Last modified: Wednesday, August 22, 2001. Send comments to Dr. George Corliss (George.Corliss@Marquette.edu)