more on Pentium bug

[David G. Hough at validgh]

There is a long string of interesting articles in comp.arch.arithmetic.
Examples have been found of single-precision operands whose quotient has
a relative error of 3e-5, ( eg 5505001/294911),
which were readily visible in commercial spreadsheet programs.

It's now on the front page of the business section of the Mercury News.
How long until page 1 of the Wall Street Journal?

A colleague who called Intel for a replacement chip was told there were
150,000 requests ahead of him.

The purpose of harping on this is not to bash Intel so much as to put the
fear of bugs into all the other chip makers and into end users.
As Cleve Moler suggested, this kind of problem means that NO extensive
numerical computations can be trusted; any results produced on buggy Pentium
systems need to be independently verified, even though the statistical
probability of incorrect conclusions
due to this division bug is orders of magnitude less than the statistical
probability of incorrect conclusions due to optimizing compiler bugs.

Intel's marketing positioning is indicated in the Mercury News article:

Dean Takahashi, SJ Mercury News, 23 Nov 94, page E1:

Theoretically, Pentium bug should affect few


More than 2 million of the Pentium chips shipped by Intel Corp. contain 
flaw, but, the company said Tuesday, it affects only the calculations of
theoretical mathematicians.

The glitch, which has been fixed since its discovery this summer, has created
a stir on the Internet, the worldwide communications network used by the
scientific community.

Howard High, a spokesman for the Santa Clara-based chip manufacturer, said the
bug in the chip's ability to calculated extended mathematical problems was
discovered - and fixed - this summer.

In creating the Pentium's circuitry - which contains more than 3 million
transistors - designers made a small flaw in a so-called floating point unit,
which performs math functions.

As a result, the Pentiums can make errors in equations involving calculations
to the ninth digit on the right side of the decimal point.

Even most engineers and financial analysts require accuracy only to the fourth
or fifth decimal point, High said.   Spreadsheet and word processor users
need not worry.

High said Intel repaired the error at a cost of perhaps several hundred
thousand dollars.   At the time, Intel had shipped about 2 million of the 
estimated 5 million or more Pentiums sold so far.

But the glitch has been the subject of hundreds of message on the Internet,
many of which criticized the company for failing to acknowledge the bug.
Others questioned the rarity of the problem.

"I know it's buzzing all over the Net.  But there are maybe several dozen
people that this would affect," High said.  "So far, we've only heard from
one.  It's reasonably rare."

High said that a theoretical mathematician with a Pentium machine purchased
before the summer should be concerned.  Intel, he said, will replace the chip
for anyone who shows they need an extremely high degree of accuracy.