This report found on UseNet and written by 
DataQuest (nobody knows them) was distributed 
by Intel Corp. (probably to the PC manufacturers).
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SPECIAL REPORT: The Great Pentium Fire Drill
     DQ MONDAY  December 12, 1994

  In this article, we cover the following topics related to the
Pentium floating-point divide bug:

o     The bounds of the bug
o     The importance of the bug
o     The perception of the bug
o     The role of the Internet
o     Why a total recall is dangerous to the industry
o     Intel's competitors
o     What Intel should do, and what it is doing
o     The software fix
o     The long-term effects of the problem
o     What a system manufacturer should do


                    The Bounds of the Bug

  It turns out that there were some small design errors in the
divide hardware in the Pentium's floating-point calculation
unit. These errors lead to incorrect results in certain
calculations that involve floating-point division. The errors
are extremely small--in many cases, insignificant--and occur in
approximately one out of every billion calculations involving a
reciprocal. For the set of all divisors and dividends, we accept
Intel's claim of one failure in every nine billion pairs.
  The most famous calculation, now known as Coe's Ratio, and
undoubtedly the most common single division performed on the
Pentium, is 4195835/3145727. Developed from a thorough study of
the Pentium's problem and selected for its worst-case nature,
this calculation should generate a result of 1.33382045; Pentium
chips afflicted with the divide problem will result in an answer
of 1.33373907, representing an error in the fifth significant
digit. Internet correspondence indicates that this is about the
largest error obtainable, and that there are approximately 1,738
unique pairs that can generate an error with this big. As the
total number of pairs is about 4x10(27), the chance of actually
hitting an error this big is vanishingly small. The other errors
occur in the sixth decimal place and further out, reportedly
randomly distributed.

                  The Importance of the Bug

  It is extremely difficult to contrive a situation in which the
divide error could manifest itself in a way that is material to
an end result. This is because the error is normally very small,
occurs at a rate that is extremely rare, and should have no
effect on the huge majority of Pentium users. The only class of
user likely to be affected is that of mathematicians working in
the field of number theory, the class of user from which the bug
was originally reported.
  Clearly, users of a Pentium-based system designing devices
where a divide error could conceivably be life-threatening-- for
example, a bridge, a ship, or a plane--should consider an
upgraded part even though the error is unlikely to occur and, if
it does, is effectively certain to be insignificant. Much
engineering design work involves iterative calculations that
work toward a solution. In these cases, the likelihood of the
bug occurring is increased, but its effect is totally negated by
the subsequent iterative calculation.  If the flaw were to
somehow cause a nonconvergence, the process would be started
over with a new set of initial conditions, and the error would
be eliminated.
  Financial users could conceivably be affected by the bug.
However, the size of the error is again likely to be immaterial,
representing hundreds of dollars in a million- dollar
transaction. Although larger transactions could be affected, no
financial institution would allow a transaction to take place
without some level of cross-checking. The cross- check process
would inevitably surface the error, and the rarity of the bug
would prevent compensating errors from occurring or for multiple
errors to compound.
  In summary, the low level of the error relative to real-world
situations, coupled with the extreme rarity of the bug,
guarantees that even calculations involving lives and money are
safe on a Pentium. Numerologists and some extremely theoretical
physicists, however, stand at risk of producing bad results and
should request replacements.
  On a final note, we observe that many Pentium users--and all
Power Mac users--run their systems without parity checks on the
memory subsystem. Dynamic memories exhibit a very rare soft
failure in which a bit flips from a one to a zero or vice versa,
the result of an encounter with an alpha particle. A typical
system will encounter this change once every few years; all
systems are susceptible to the problem, and it is completely
random. Most of the time, this flip doesn't matter because it is
overwritten by new data or in an area of the memory that is not
in use. However, intensive numerical calculations that fill
memory with intermediate values could turn up an occasional
incorrect answer once every few hundreds of machine years. We
believe that this class of error is as significant or more so
than the Pentium divide bug, as it occurs more frequently and
can result in a much larger change in the number.

                  The Perception of the Bug

  Having established that the bug itself is immaterial (and we
would be happy to talk about this at great length--it is
extremely difficult to contrive a real-world calculation in
which it matters), we now turn to the perception of the bug in 
the press. Many of the recent writings on the subject--in many
cases by people who should know better--treat the problem as if
the Pentium cannot perform simple arithmetic, and that all
applications that do calculations are exposed to some
significant risk. Part of the problem here lies with Intel's
engineering-driven PR effort, which created the impression that
Intel would anoint the chosen few who would receive updated
parts; this tactless bungle touched off the initial Internet
furor from which most of the press articles drew.

                   The Role of the Internet

  There is also a lesson on the use of the Internet here. The
nature of electronic mail is such that it strips personal
interaction from communication. Without this interaction, simple
statements or even typographical errors can be interpreted as
strong opinion and can touch off torrents of strongly-worded
messages. There are few low-energy opinions on the Internet, and
just a few angry people can stir up an electronic uproar. We
believe that the single greatest PR error was the posting of
Andy Grove's response on the Internet. The Internet response was
strong and negative; many writers took their tone from the
Internet correspondence. We believe that a press conference 
would have been much more successful and could probably have
dampened much of the negative reporting that was in essence
driven by the Internet.

       Why a Total Recall Is Dangerous to the Industry

  Several writers have suggested the idea of a total recall of
the part. We at Dataquest believe that this is an imprudent and
irresponsible suggestion; the severity of the bug does not merit
the slightest consideration of the idea, and a recall could
damage the structure of the entire PC industry and all its
participants, not just Intel itself. The size of the problem
involves not only a couple of million Pentium chips in the
field, but a total of perhaps 6 to 7 million units built and in
the pipeline.  Although Intel could afford the monumental cost
of replacing existing parts, not shipping the pipeline inventory
would delay shipments of Pentium processors by several months.
This delay would result in a stall in sales as Pentium leaders
such as Packard Bell, Gateway, and Dell stopped selling Pentium
systems (which are rapidly becoming the bulk of their revenue).
The inventory that these companies and other Pentium leaders
hold would drop in value, resulting in a substantial loss and
potentially forcing them out of business. This shock wave would
propagate back through the supply channels and result in fewer
competitors in the market; higher prices and slower
technological progress are the final result of such a change. In
short, a bad thing for users and all players in the PC business
(including the journalists whose salaries are funded by
advertising).

                     Intel's Competitors

  Intel's competitors have remained silent on the issue; this
could have happened to any of them. IBM pulled a coup by
offering to replace all Pentium chips that it has shipped,
sneaky in that IBM has not shipped very many Pentium chips (we
would suspect that Ambra machines aren't covered under this
deal). AMD, Cyrix, NexGen, and even the PowerPC group have
wisely kept their heads down, choosing not to pillory Intel
(although Intel has done a good job of making its own burden on
this one). [NOTE:  THIS ARTICLE WAS PREPARED EARLY MONDAY,
editor]
  We also note that a Pentium vacuum is an opportunity for no
one. The competing parts aren't available, and even if they
were, it would not be economically viable for competitors to
ship low-yield advanced die (that is, early versions of the M1
from Cyrix and K5 from AMD) instead of profitable 486 parts.

          What Intel Should Do, and What It Is Doing

  The way to be clear about something is to put up money. In
stating that the Pentium is good for almost all users, Intel
stands liable for a financial or other loss that a user may
incur as the result of a faulty Pentium calculation. Intel's
obligations to its shareholders mandate that this decision be a
good one.
  The first line of defense is the Intel Lifetime Warranty,
under which Intel promises to replace a Pentium if ever the user
needs it because of new software or new applications. Coupled
with a fair return policy, this is a good compromise for the
user and Intel. In fact, we believe that the Lifetime Warranty
is a natural extension of Intel's newly found relationship with
its customers' customers and will propagate through succeeding
generations of processors and turn into yet another entry
barrier.
  Intel has established an effective telephone system to handle
the replacement policy. The lines are open 24 hours a day, and
Intel has contracted third-party telephone support to screen
incoming calls, resolving the issue of busy phone lines.  We
believe that a user with a genuine need for the part could get a
replacement without difficulty, and that Intel is erring on the
side of caution. Numerologists, financial users, and designers
working on projects that could conceivably put life or property
at risk are almost certain to qualify for replacement parts; our
discussions with Intel indicate that the problem will be handled
fairly and efficiently, and we suspect that users who make
enough fuss will get a new part whether they need it or not.
Intel clearly intends to make its customers' customers happy.
  The only other thing that needs to be taken care of is the PR
side. We believe that Intel has made advances in cleaning up its
previously ruthless image, but this debacle shows that there is
much progress to be made. Intel will certainly have to put up
with--and learn to smile at--many Pentium jokes over the next
couple of years. This development of a softer side will be a
good thing for Intel, and for the industry as a whole.

                       The Software Fix

  Intel, in conjunction with some of the individuals that have
developed the best understanding of the problem, is developing a
software fix for the problem. This fix will take the form of a
floating-point library that will be used in place of the
standard Pentium floating-point calls and will be provided to
software manufacturers. The library will use fast screening
techniques that let most calculations proceed using the Pentium
hardware; divide pairs that could cause a problem will be
checked in more detail, then numbers that truly fail will be
processed in such a way as to generate the correct result. This
approach will slow down the Pentium's divide operations
somewhat, but it is unlikely to be noticeable.
  Software manufacturers will incorporate the library routines
into their software and will provide patches via BBS or online
services that guarantee accurate results in all cases for users
who depend on floating-point accuracy.

             The Long-Term Effects of the Problem

  Our belief is that this issue will subside over the next few
weeks as users realize that, despite the press hype and PR
fumbles, this error just doesn't matter. It is the equivalent of
a whoopee cushion, noise and action leaving Intel red-faced and
floundering but with no real damage to its business or the PC
business as a whole. However, all processor designers have
learnt a hard lesson about testing of their parts and why
engineering approaches to PR problems don't seem to work out too
well.

             What a System Manufacturer Should Do

  Keep shipping the product, but work with Intel to ensure that
some supply of replacement parts will be available to satisfy
critical users. Train customer service agents to help customers
understand the problem, passing out the Intel numbers if
necessary. The Intel FaxBack documents are a good first line of
defense, and system manufacturers can send these out on their
own. Intel would like to do all the screening itself, but we
believe that system manufacturers should be responsible for
their own destiny and need to play an active part in helping
their customers understand the issues. It is entirely possible
that Intel's part in resolving the issues for unhappy customers
could further consolidate Intel's brand equity in the user base;
this is not necessarily in the best interest of system
manufacturers.

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