FYI: Pentium FPATAN can lose 36 bits (out of 64)

[David G. Hough at validgh]

I had heard that the FDIV problem showed up in atan and log, but this may be
the first independent confirmation.   It certainly complicates Cleve
Moler's problems building a bullet-proof workaround.

But I think the atan problem reinforces the gravity of the FDIV bug in an
unexpected way:   while log and atan are only used in esoteric calculations
like computing mortgage payments and deciding which direction to fly, as
far as I know - please correct me if you know better - there is no particular
reason to suspect that the patterns of operands supplied to the divider
from within the elementary transcendental functions are inherently unusual.
So the probability of hitting the FDIV bug in random operands of general
scientific computation is probably not much different from hitting in
while testing transcendental functions.

The best-publicized examples of the FDIV bug have involved small integer
operands because they seem more relevant to the general public, but I doubt
that there are very many cases of dividing pairs of small integers in the
transcendental functions.    The inference I draw from the transcendental
bugs is that most general
scientific calculations that run all night on a Pentium WILL encounter the
FDIV bug, although the odds are small but non-zero that wrong conclusions
will result.

Most of the Pentium jokes I've heard are pretty dumb, but this one via
gnuatoad.com should
elicit nervous chuckles or groans.   It's just a matter of time before
some ambitious politician tries to make some hay out of Pentium one way or 
another:

From: bugsawarlock.win.net (Mark Hittinger)
Date: Mon, 05 Dec 94 01:04:09 -0800

        November Election results may be due to Intel Pentium bug

An anonymous source in the Democratic Party has revealed that the sweeping
landslide victory of the Republicans in November may have been due to an
obscure bug in the Intel Pentium computer chip.
 
Upgrading the nationwide vote counting system to the latest technology was
one of Vice-President Al Gore's "Reinventing Government" initiatives.  This
change was meant to reduce costs and streamline operations, however, the
computer glitch may have cost the Whitehouse dearly.
 
A spokesman for the Democratic Party denied the rumor that several thousand
Power-PC's had been purchased as part of a vote recount effort.
 
When questioned about the news Senator Bob Dole (r) commented that he believed
the Intel Pentium chip was far better than anyone had thought.  A short
statement released by Newt Gingrich's office indicated that "the Democratic
party has always sought to divide America and that this discovery of an
FDIV bug in the Intel Chip was clear evidence of the moral decay of our
society."

At a Motorola Plant in Austin, Texas Ross Perot told an angry crowd that
according to his new calculations the deficit is actually 14 times larger than
the government has been telling us.  He praised his staff for staying
up all night and performing the calculations by hand.

In late breaking news today legal briefs were filed in Chicago by former
senator Dan Rostenkowski's attorneys which claimed that the irregularities at
the House Bank and the House Post Office were actually due to Pentium chip
calculation errors.  Sources in Attorney General Janet Reno's office reveal
a furious behind the scenes effort to reload the whitewater investigation
spreadsheets in order to double check the results.