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InfoWorld: Sun researchers: Computers do bad math: December 17, 2003: By : Platforms:
"Mathematical errors are far more common in the computer industry than most people realize, said Greg Papadopoulos, Sun's executive vice president and chief technology officer. While his company is normally the first to accuse Microsoft Corp. of shoddy operating system design, bad math and not Windows is sometimes behind those unexplained PC crashes, he admits.

'There are a lot of errors that happen in machines that go undetected,' Papadopoulos said. 'Sometimes a machine just goes away and freezes. You always blame it on Microsoft. We do, too. It's convenient. It's convenient for Intel, too.'

'It's a dirty secret. Floating-point arithmetic is wrong,' said John Gustafson, a principal investigator with Sun, based in Santa Clara, California. 'It only takes two operations to see that computers make mistakes with fractions.'

The problem that Gustafson and Papadopoulos referred to stems from the fact that the binary mathematics employed by computers has a hard time accurately representing certain numbers. Fractions, for example, are particularly tough, because they often involve non-terminating numbers that are impossible to accurately express in binary format.

Dividing two by three on a calculator illustrates the problem. The fraction 2/3, when represented in a computer, is inevitably rounded up, making the last digit a seven.

In the case of the Gulf War incident, the Patriot battery's computer rounded a similar, non-terminating number in order to calculate time. But by shaving off a few digits during every calculation, the battery also shaved off a bit of time. After one hour, the Patriot's clock was off by .0034 seconds. On Feb 25, the computer had been in operation for 100 hours straight, and its clock was off by over one third of a second, enough to cause it to miss the incoming Scud."

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