Conference 7.286::digital

    Yeah, but it runs DOS applications slower than a 486.

   <<< Note 3340.1 by ODIXIE::LUBER "I have a Bobby Cox dart board" >>>
    
        Yeah, but it runs DOS applications slower than a 486.
     
    	Doesn't the next version of NT sort out that slowness problem?
    
    	Also, why don't we get in there and sell them the idea Alpha, for
    them to make under Licence and then co-develop the Alpha and its
    eventual replacement?
    
    				Malcolm. 

    Just as some of the Intel processors are starting to slide into history, 
    so will some of the older operating systems in my opinion.  I believe it
    is the nature of the industry (hardware and software).  The days of
    paper tape/cards and the like have been replaced with windowing
    environments.  
    
    The trick is predicting and anticipating the future and positioning 
    yourself where the most money can be made.  They future will be
    characterized operating systems and languages which are able to take
    full advantage of the new processors.  

HP, which just announced very strong quarterly results, is hedging its bets and
keeping a foot in both camps: allying with Intel for future 64-bit RISC h/w,
and with Apple and IBM for future OO (Taligent) s/w.  Maybe because of their
instrumentation and printer businesses, they seem to have a better strategic
handle on the concept of diversification.  They're certainly doing something
right, if you compare their earnings to ours.
								- paul

P.s.  but the person who grabs market share as an information superhighway
	supplier will be the ultimate winner...something that only Charlie
	Christ seems to be focused on here at Digital

    An interesting topic.  Lately, I have noticed that Pentium machines
    have disappeared from local retail stores.  They now only carry 486
    machines.  This must be frustrating for Intel, who is trying to make
    Pentium the desktop standard.  In fact, the local stores NEVER carried
    P90 machines -- only P60 machines.  

    A friend of mine who recently got his EE from George Mason University 
    has been intimately involved with board work using state of the art chips.  
    
    He said that virtually everyone hated the Pentium "environmental" work - 
    basically the chip needs to be double heat-sinked along with the addition 
    of multiple cooling fans, etc. to keep the systems from overheating.  
    
    He RAVED about how cool the Alpha ran!  No extra heat-sinking, no fans.
    He said that the professors and students alike were awed by its speed.  
    
    Congress has just granted $13 million to GMU for a new supercomputer
    center.  Digital really needs to take advantage of this opportunity.
    Assuming that we still have a sales rep for the account...

    The Pentium P60 runs hot because it is a 5 volt chip.  Intel's new and
    improved version, the P90 is a 3.3 volt chip that doesn't have the same
    cooling problems.  That's one of the reasons why Intel is unloading
    P60's at fire sale prices (no pun intended).

    >>> Intel is petering out
    
    
    Yeah, right - Andy Grove is quaking in his boots!  I guess that means
    Digital has a real chance with Alpha now.
    
    NOT!

    
    	Hey-----
    
    	Intel is the hot chip right now. We are selling them like hotcakes.
    This is the third month in a row now that Kanata is sold out of
    production.
    	Alpha could very well be the hot chip three years from now.
    Remember when Intel first came out with the 8086, Motorola was
    eating their lunch. Now Moto makes microprocessors for Apple and
    that's about it in the commodity box space.
    	So who knows? In my 25 years in this business, I've learned one
    thing for sure. Today's hot product will not be tomorrow's.
    
    		the Greyhawk

Let Intel sell - let's try to head off PowerPC.

			Steve

    
    re .9  Yes indeed, ohhh marketing, whats the plan?
    
    Just got off Compuserve, Investors forum.  Seems people are starting
    to talk about Intels future, and guess what?  Alpha was discussed in
    a very positive light.  As usual, it was word of mouth.  A fellow's son
    is using Alpha, and he likes it!

    re .5
    
    Here in Northern California, even Circuit City is chock full of
    Pentiums. Must be the proximity to Intel. Fry's of course has tons of
    them too.
    
       e

    
    <<< Here in Northern California,
    
     Now I know why you all have so many forest fires.
    
    <<< Fry's of course
    
    That explains everything!
    
    -Mike Z.

Like Greyhawk, I've got over 25 years in this business as well, and my
observation is that the real commercial breakthroughs come by making
industry history.

DEC was a perfect example, having done so in every hardware generation and
making bundles in the process.

Obviously, the microprocessor was industry history, and Intel has done a very
good job of milking that niche, and for quite a number of years, as well.

Clearly, then, for Alpha to succeed, it must make history.  It will not be
enough to be the first 64-bit chip, it must become the standard.  That does
NOT mean competing with Intel for the mass desktop market.  It means
competing with whomever for markets that are just beginning to open, such
as the Info Superhighway or Multimedia, where 32 bits will prove to be
non-competitive.

But the industry has changed in a significant way from the era of the PDPs
or the VAX.  It is no longer enough to build a box, fill it with system
software, and shove it out the door.  It has to be full of solutions.  I
wonder if Digital is capable of competing in this kind of a world.

Steve

    re .14
    Alpha wasn't the first 64 bit chip.  Remember the R4000's we used to
    sell before Alpha?  kb

    I may be wrong, but I seem to recall after working on the R4000/R4400
    that EV4 already existed while the R4000 was still vapor (I'm including
    the R4000PC version that does not have a secondary cache interface and 
    sampled first). So it seems according to my memory that Alpha was first
    by a wide margin. When Digital "announced" exactly may paint a
    different story.
    
    Dave
    
    
    

    From PC Week August 22, 1994 RISC makers hurting from scant OEM
    support, which is decling.
    
    A chart illustrates what Dataquest, Inc thinks will happen:
    
    		Pentium     PowerPC     Alpha     MIPS     SPARC
    	1994	5.7M        1.25M	0.1M      1.3M     0.5M
    	1995	17.3M	    3.75M	0.35M	  1.7M	   0.575M
    	1996	30.1M	    5.62M	0.8M	  2.1M	   0.575M
    
    
    At least we're selling more than SPARC.

    	Actually, Alpha has the highest growth rate of all of them there,
    with a growth factor of almost 3* per year. If you extrapolate the
    growth curves you can calculate in which year Alpha will be selling
    more than all the rest put together.

    "At least we're selling more than SPARC."
    
    Since those dates are in the future, it looks like "we're
    expected to sell more than SPARC" would be more appropriate.
    
    ed

    RE: .18
    
    I seem to recall the extrapolations which showed the year that we
    (Digital) would pass IBM, based on our grow rate in the late 80's. Of
    course in those days both charts were pointing in an upward direction.
    
    OFWAMI ;^)

    	I also remember when IBM could have bought DEC with their previous
    month's profits. DEC has grown very rapidly in the past. I don't
    believe that sort of extrapolation either, but the chart wasn't a picture
    of total gloom.
    
    	Someone will supercede the Intel architecture eventually, and I
    don't see why it shouldn't be us. I have seen incredibly high-tech bows
    and arrows, and they are still used for at least one of their
    traditional applications - target shooting. Somehow that doesn't seem
    to be where someone equiping a modern army seems to spend most of his
    money, though. Maybe the bow makers have slipped behind on the
    cost/person-killed curve. Intel has a fine future, and 13'th century
    bow maker could probably show you that more bows are being made and
    sold now than ever before. It is a growing business.

    
    Before we start using growth rate as a measure of success, suppose the
    Digital part of the chart looked like this:
    
    		Digital
    1995	   1	(i.e., sold one Alpha chip in 1995)
    1996	   2    
    1997           4
    
    Then, Palmer could tell WallStreet that we are "on track" and Alpha
    sales have grown 100% in 1996 and 200% in 1997.  But he won't say that
    we only sold 4 in 1997.  Is this good news?
    
    Dennis
    

>  Is this good news?

Combined with the fact that Alphas outsold (declining) VAXes, we can hope...
    

I'm sure this has been asked before, but can't we do something with Alpha's 
PAL code to make it look like an Intel chip and run DOS & Windows in a 
quasi-native mode? That would certainly allow us to increase our volumes.

    	The short answer is that we already have it. About the only thing
    special in PAL code is that you take a few extra instructions to switch
    in and out of kernel mode. Using PAL code for something that you can do
    in user mode is actually slower. The emulator on NT does the Intel chip
    emulation already, as far as is reasonable, and if you moved it to PAL
    code you wouldn't improve its speed. The instruction set emulator
    already exists.
    
    	I think currently the emulator can get close to 386 speed, so if we
    can sell Alpha chips for less than 386s, and also spend the software
    effort moving the existing emulator to kernel mode then we could have a
    good market.
    
    	The alternative of emulating an MS-DOS environment to permit *any*
    MS-DOS application to run would be a nightmare. For example, many of
    them assume they can patch interrupts for devices that only they
    understand.
    
    	In theory it is quite possible, but in practice nobody wants such
    slow performance. Alpha machines give good performance on applications
    when *most* of the code executed has been compiled with a compiler that
    generates Alpha code. With NT all of the operating system code has been
    compiled with a compiler that generates Alpha code, so an application
    that spends most of its CPU time in system or library calls will run 
    well even if the user code is emulated. If you can put the source code
    through a native compiler then it will run fast!  And we now have
    several native compilers for NT.
    
    	This sort of thing is always possible. VMS FT3 *only* ran on a
    (slightly modified) PDP-11/70 since a VAX machine hadn't been built
    then. FT1 and FT2 versions ran on an emulator on a DECsystem-10, I was
    told, but nobody pretended that the performance was good.

    In my mind, .25 thinking is our problem.  
    
    We still expect users to change to accommodate our technology rather
    than produce technology that can be used with out the user having to
    adapt.  
    
    I started out in PCs with a Rainbow running Lotus 123, Wordperfect,
    and dBase.  When I finally gave up on the Rainbow and converted to a
    286 system, I had to spend major bucks to replace the software with
    versions that would run on the 286 platform.  That same software still
    runs on my current 486 system, and if I upgraded to a Pentium, it will
    still run.  If I had to purchase new versions of software to run on an
    Alpha system, I would be looking at a bill of $2,000 or more, IF Alpha
    versions were available.  Otherwise, the performance of my current
    versions will be a step backwards, to "near" 386 performance.
    
    Not my idea of progress.

    	I'm glad .26 got the irony. Eventually the Intel x86 architecture
    *will* be dead, just as their MCS-4 architecture is now dead. No
    architecture lasts forever, and historically 10 years has been typical
    for good architectures in the computer industry.
    
    	There was a PDP-8 emulator on the PDP-11s, VAX systems have
    capabilities for running PDP-11 software, and some of the features of
    the Alpha architecture are there mainly to allow easy emulation of VAX
    behaviour (like supporting 32-bit mode VMS). I think I even remember an
    MCS-4 emulator on the PDP-8.
    
    	The fact that anyone even suggests emulation means that the
    architecture is dying. I would consider buying Intel shares when
    someone suggests emulating Alpha architecture on an Intel architecture
    of the future.
    
    	We are not expecting users to change to accomodate *our*
    technology. We *know* they will change to take advantage of technology
    improvements. Intel's next step is to leapfrog the Alpha architecture
    and ship with an emulator that will give nearly Pentium performance,
    but that is several years away.

RE: .26

>Not my idea of progress

	Get ready to spend alot of money over the next few years. You'll
	be purchasing WIN32 apps. Why? So you can realize the benefit of
	32 bit computing. (Microsoft-speak)

	Yea, you'll still be able to run your 16-bit apps (DOS/Windows)
	but in reality, most people will shell out the $2000 it's going
	to cost to move to WIN32.

	Only Microsoft can make you want to change like this. I think they
	call it marketing.
							mike

Today, Intel is dominant because of the vast amount of software, and
the principle below:
	software once developed and QA'ed, will only support a single
	architecture.

I firmly believe that this principle will not be true in the future
(very likely in the next 10 years).  Technologies that could
contribute to this change include ANDF (Architecturally Neutral
Distribution Format).  Market realities will also force this
decoupling of hardware and software, especially as hardware functionality
becomes becomes disproportionately ecclipsed by software availability.
 Once this principle is broken, the rules of the market change
forever:
	hardware volume is determined more by inherent capabilities
		of the hardware, rather than application availability

If this principle was broken today, Sun would be instantly out of
business.  If it had been broken in 1990, Digital would have been
out of business.

An article appeared on Fri 02 Sept in the Gaurdian Newspaper (UK) about
the Intel Chess Grand Prix.It was about a chess match between the World 
Chess Champion Gary Kasparov and the Pentium Genius Computer which of
course the computer won, the first time that Kasparov has been beaten 
by a machine.
        Above the article is a picture of a dejected looking Kasparov
at the table with the Intel logo and Pentium Processor clearly
displayed and the headline in huge type saying

       CHECKMATE FOR THE SUPERCHIP

This to me seems an inspired piece of promotion and there have been 
further stories in saturdays papers.

>An article appeared on Fri 02 Sept in the Gaurdian Newspaper (UK) about
                                           ^^^^^^^^
Check your spelling, that should be `Grauniad'  :)

Chris.

    >>An article appeared on Fri 02 Sept in the Gaurdian Newspaper (UK) about
                                                ^^^^^^^^
    
    Well Chris, seeing as he mispelt Guardian, he was on the right tracks
    anyway.
    
    
    Max.
    

         Extracted from the Sunday Times (4th September):
    
    	The Pentium processor computer that beat Garry Kasparov, the world
    chess champion, was defeated yesterday in the semi-final of the Intel
    Speed Chess Grand Prix by Viswanthan Anand, an Indian grandmaster.
    
    
    

    With these chess computers, it's the software, not the hardware,
    that matters.  I suppose the hardware vendors like to ignore that
    for the publicity, though.
    
    					Steve	

    re .34
    
    Both software and hardware are important, as this is a timed match. The
    same software on a 486 or a VAX would probably not have done so well as
    it would have been forced to make moves without doing so much analysis.
    It would be interesting to try a match between different hardware
    running the same software (Pentium V Alpha Chess match ? That would be
    VERY interesting).
    
    Andrew

    Many VAXes would be faster than Pentium.
    
    Of course, they are also more expensive.  :-)
    
    ed

    Re .35
    
    In the Dutch computer chess championship towards the end of last year,
    an AXP system came first with a Pentium second. In the game between
    them the AXP system won. The software was not the same, but the AXP's
    program had been ported from DOS.
    
    Peter

	.35 has got the right angle on this (admittedly effective)
	piece of unfortunate Intel marketing.

	In fact, even the quality newspapers (sorry Grauniad) managed
	to cut to the chase on this.  The Weekend FT ran a long article
	in the non-business section, stating (from my memory) ;

	"with the remaining potential in silicon and software development,
	 it is only a matter of time before such fixed environment
	 matches between man and machine are seen to be as irrelevant as 
	 a sprinter trying to outpace a F1 racing car"

	The FT goes on to state that this is a pure speed game.  The
	software is already very good and that it is a "matter of balancing
	short term (speed driven) tactics against long term chess strategy.
	It is debatable whether the same software (and chip) could 
	consistently beat GrandMasters under tournament conditions"

	What is far more interesting in their writer's opinion is computers
	(and software) to solve real word problems like deciding whether
	somebody is a good credit risk.
	

	Also, they spice up the business angle by commenting that the winning
	technology was a Pentium - "affordable by the masses at around
	$2000 configured in a box".  This is the challenge for Alpha.	

/Chris.

>>    Many VAXes would be faster than Pentium.

perhaps as few as two or three of them would be faster than a Pentium :-)
    

    FWIW, given that computers will continue to go faster and cheaper, 
    I think chess will eventually go the way of tic-tac-toe ...  I can see
    it now.  After the first one or two moves, both computers recommend
    quitting, agreeing that the game will likely result in a draw ...
    
    Steve

    Q&A:  THE PENTIUM FDIV BUG
    
    Q:  How many Pentium designers does it take to screw in a light bulb?
    A:  1.99904274017, but that's close enough for non-technical people.
    
    Q:  What do you get when you cross a Pentium PC with a research grant?
    A:  A mad scientist.
    
    Q:  What's another name for the "Intel Inside" sticker they put on
    Pentiums?
    A:  The warning label.
    
    Q:  What do you call a series of FDIV instructions on a Pentium?
    A:  Successive approximations.
    
    Q:  Complete the following word analogy:  Add is to Subtract as
    Multiply
        is to:
            1)  Divide
            2)  ROUND
            3)  RANDOM
            4)  On a Pentium, all of the above
    A:  Number 4.
    
    Q:  What algorithm did Intel use in the Pentium's floating point
    divider?
    A:  "Life is like a box of chocolates." (Source: F. Gump of Intel)
    
    Q:  Why didn't Intel call the Pentium the 586?
    A:  Because they added 486 and 100 on the first Pentium and got
        585.999983605.
    
    Q:  According to Intel, the Pentium conforms to the IEEE standards 754
        and 854 for floating point arithmetic.  If you fly in aircraft
        designed using a Pentium, what is the correct pronunciation of
    "IEEE"?
    A:  Aaaaaaaiiiiiiiiieeeeeeeeeeeee!
    
    
    TOP TEN NEW INTEL SLOGANS FOR THE PENTIUM
    
      9.9999973251   It's a FLAW, Dammit, not a Bug
      8.9999163362   It's Close Enough, We Say So
      7.9999414610   Nearly 300 Correct Opcodes
      6.9999831538   You Don't Need to Know What's Inside
      5.9999835137   Redefining the PC -- and Mathematics As Well
      4.9999999021   We Fixed It, Really
      3.9998245917   Division Considered Harmful
      2.9991523619   Why Do You Think They Call It *Floating* Point?
      1.9999103517   We're Looking for a Few Good Flaws
      0.9999999998   The Errata Inside
    
    :)

    Remember that what we now call the High Memory Area portion of Extended
    memory is due to a BUG in the microcode of the original 80286's... they
    soon learned to call it a FEATURE and it has been replicated to all
    80x86 CPUs since...
    
    Maybe this is just the beginning of a new FEATURE?
    
    tony

{Forwards removed]

From: [email protected] (Tarl Neustaedter - SMCC Software)
To: [email protected], [email protected], [email protected],
        [email protected]


You may have seen the pentium flaw (FDIV incorrect precision) that has
resulted in so much intel bashing. Intel has handled it _very_ poorly,
basically saying "unless you are very technical, you won't notice it,
so go away and stop bothering us".

Some of the collected bashing:

> From: [email protected] (Alex Chun)
> Newsgroups: comp.sys.intel
> Subject: THE TOP TEN REASONS TO BUY A PENTIUM MACHINE  :-)
> Date: 29 Nov 1994 05:25:54 GMT
> Organization: University of Pennsylvania

THE TOP TEN REASONS TO BUY A PENTIUM MACHINE
============================================

10. YOUR CURRENT COMPUTER IS TOO ACCURATE

9.  YOU WANT TO GET INTO THE GUINNESS BOOK AS
    "OWNER OF MOST EXPENSIVE PAPERWEIGHT"

8.  MATH ERRORS ADD ZEST TO LIFE

7.  YOU NEED AN ALIBI FOR THE I.R.S.

6.  YOU WANT TO SEE WHAT ALL THE FUSS IS ABOUT

5.  YOU'VE ALWAYS WONDERED WHAT IT WOULD BE
    LIKE TO BE A PLAINTIFF

4.  THE "INTEL INSIDE" LOGO MATCHES YOUR DECOR PERFECTLY

3.  YOU NO LONGER HAVE TO WORRY ABOUT CPU OVERHEATING

2.  YOU GOT A GREAT DEAL FROM JPL

And the #1 reason to buy a Pentium machine:

1.  IT'LL PROBABLY WORK


From: [email protected] (DMethvin)
Newsgroups: comp.sys.intel

Q&A:  THE PENTIUM FDIV BUG

Q:  How many Pentium designers does it take to screw in a light bulb?
A:  1.99904274017, but that's close enough for non-technical people.

Q:  What do you get when you cross a Pentium PC with a  research grant?
A:  A mad scientist.

Q:  What's another name for the "Intel Inside" sticker they put on
    Pentiums?
A:  The warning label.

Q:  What do you call a series of FDIV instructions on a Pentium?
A:  Successive approximations.

Q:  Complete the following word analogy:  Add is to Subtract as Multiply
    is to:
        1)  Divide
        2)  ROUND
        3)  RANDOM
        4)  On a Pentium, all of the above
A:  Number 4.

Q:  What algorithm did Intel use in the Pentium's floating point divider?
A:  "Life is like a box of chocolates." (Source: F. Gump of Intel)

Q:  Why didn't Intel call the Pentium the 586?
A:  Because they added 486 and 100 on the first Pentium and got
    585.999983605.

Q:  According to Intel, the Pentium conforms to the IEEE standards 754
    and 854 for floating point arithmetic.  If you fly in aircraft
    designed using a Pentium, what is the correct pronunciation of "IEEE"?
A:  Aaaaaaaiiiiiiiiieeeeeeeeeeeee!


TOP TEN NEW INTEL SLOGANS FOR THE PENTIUM
- --------------------------------------------------------------------------

  9.9999973251   It's a FLAW, Dammit, not a Bug
  8.9999163362   It's Close Enough, We Say So
  7.9999414610   Nearly 300 Correct Opcodes
  6.9999831538   You Don't Need to Know What's Inside
  5.9999835137   Redefining the PC -- and Mathematics As Well
  4.9999999021   We Fixed It, Really
  3.9998245917   Division Considered Harmful
  2.9991523619   Why Do You Think They Call It *Floating* Point?
  1.9999103517   We're Looking for a Few Good Flaws
  0.9999999998   The Errata Inside


----- End Included Message -----

        While the Intel Pentium flaw is much more serious, I do hope
        that we correct the fact that our external World Wide Web
        home page says:

        	This server was last updated: Wed Nov 24, 1994.

        Bob

    IBM, who doesn't sell a lot of Pentiums, pulled a PR coup and
    announced that it would be replacing all of theirs in the field.
    
    Buttheads.
    
    ;-)
    Kratz

    Can we afford to do the same?  Can we afford NOT to?
    
    Another bash I heard: At Intel, quality is Job 0.9999.
    
    But funny as they are, are we going over the line by repeating these
    bashes?

>    Can we afford to do the same?  Can we afford NOT to?

Do we have a choice?  The warranty card for my Starion Pentium system says:

"Digital Starion(tm) PC products are warranted against defects in workmanship
and material for one (1) year commencing on the date of purchase from an
authorized Digital reseller..."

Looks to me like if I was to call 1-800-354-9000 and say that my processor
couldn't divide numbers correctly, I'd be getting a processor that could.

Course we might be able to "wiggle" out on the 3rd party warrenty exclusion,
but i'm willing to bet there's a few lawyers out there that would love to take a
case like this.

My prediction is that this is going to get very expensive for Intel.

    Could someone please help me here.  I seem to recall back in the dark
    ages at grad school doing a similar exercise on a DECSystem 20 (running
    TOPS20).  The exercise was to do some multiplication and division by
    very large (or was it small) numbers.  Mathmatically, you should have
    ended with the same number you started with.  However, they weren't. 
    The exercise was intended to illustrate the level of precision a
    computer was capable of achieving.  I think it had something to do with
    word length.
    
    Am I totally off the planet, or is Intel perhaps getting bashed for an
    inherent characteristic of the computerbeastie?
    
    Bill

Re .48, This time the problem is real (sic)
    
Re .snears at intel for bug
    
    This Intel problem with Pentium is kinda good fun, It sure is a good 
    problem not to have! Yes, we (digital) could use a break and all that, 
    but IMHO we should not be too eager to make milage out of it. 
    If anything, we can make milage about how Intel appears to deal with it,
    (or rather the lack of dealing with it) but not with the fault itself. 
    Why not? Because we live in a glass house. For example, the DEC Cobol RTL
    on Alpha has had several mathematical bugs. Not 'just 1 or 2', but more.
    Yes we have a CLD process and yes we are pro-activly shipping fixes
    and yes Cobol program mostly only deal with your and my money, not 
    with vastly more important things like the distance to the sun... ooops!.
    
    One example of our fumbling included. Just imagine (sic) if that notes
    title: "error in calculation on AXP" where to hit the newsgroups...
    
    [My apologies to my friends in Cobol Engineering for picking them
    as an example. They are not the only example. They are just the
    most recent example I happen to be aware off. I seem to recall 
    SIN and COSine stuff for fortan in a further past and more.]
    
Just an opinion....

	Hein.


           <<< CLT::DISK$CLT_LIBRARY3:[NOTES$LIBRARY]COBOL.NOTE;1 >>>
                               -< VAX/DEC COBOL >-
================================================================================
Note 2817.0               error in calculation on AXP                  8 replies
HGOVC::PETELAM                                       67 lines   4-OCT-1994 00:04
--------------------------------------------------------------------------------
	
    Could someone help on this ?
    
    same program produced different results on VAX and AXP.
    
    Thanks
    Pete
    
    
	
    - In VAX COBOL

            COMPUTE D = A / B * C
            DISPLAY D

                     A : 55.1190 
                     B : 4.1910
                     C : 6.4140
                   
            The result  D :  84355348604151753D

	
    - In DEC COBOL ON AXP

            COMPUTE D = A / B * C
            DISPLAY D

                     A : 55.1190 
                     B : 4.1910
                     C : 6.4140
            
            The result  D :  84344100000000000{

================== SAMPLE PROGRAM ================================

IDENTIFICATION	DIVISION.
PROGRAM-ID.	JUNG.
ENVIRONMENT	DIVISION.
CONFIGURATION	SECTION.
SPECIAL-NAMES.
	SYMBOLIC CHARACTERS ESC ARE 28.	
DATA	DIVISION.
WORKING-STORAGE		SECTION.
01	TEST-FIELD1	PIC	X(60).
01	A		PIC 	S99V9(16).
01	B		PIC 	S9V9(17).
01	C		PIC 	9V9(16).
01	D		PIC     S99V9(16).
01	E		PIC     S99V9(16).
01	F		PIC     S99V9(16).

PROCEDURE	DIVISION.
PROCESS-START.
	DISPLAY "" ERASE SCREEN.
ACC-RTN.
	ACCEPT A WITH CONVERSION.
	ACCEPT B WITH CONVERSION.
	ACCEPT C WITH CONVERSION.
	COMPUTE D = A / B * C.
	DISPLAY "D  :" D.
        COMPUTE E = A / B
        COMPUTE F = E * C
	DISPLAY "F  :" F.
	GO TO ACC-RTN.

    
    

Hm... do you realize that the Pentium bug has impacts beyond the PC market ?

Anyone out there fighting against SEQUENT or AT&T (ex NCR) ? Well, all their
new systems are based on Pentium .. and most of these systems typically not 
used to play DOS games on ...

  >  You may have seen the pentium flaw (FDIV incorrect precision) that
  >  hasresulted in so much intel bashing. Intel has handled it _very_
  >  poorly,basically saying "unless you are very technical, you won't
  >  notice it,so go away and stop bothering us".
    
    
    Sorry to sound stupid, but what is this FDIV Bug, and how does it
    manifest itself?
    
    Thanks 
    
    Martin 
    

>                     <<< Note 3340.51 by BASLG1::BURNLEY >>>
>    
>    Sorry to sound stupid, but what is this FDIV Bug, and how does it
>    manifest itself?

As I read the article in the 11/7/94 EE Times, the spec'd precision of 
the floating point unit is 19 significant digits.
In the calculations in question, errors show up at the 8th or 9th
most significant digit

Yep.  That's right.  A whole number divided by it's half should always have the
result of 1.33

    ... We'd have to take out another (tm) on 
    
    
    ALL-IN-1.0000003
    
    :-)
    

    Let's not confuse performing per spec and the inaccuracies you get due
    to number systems and limited word lengths.  The former is why Intel is
    in trouble.  The latter is something that is inherent with computer
    systems.  To write off the Intel bug due to the latter is wrong. 
    Simply stated, the Intel chip does not perform as it should.  This is
    independent of roundoff errors and the like that we can deal with in
    software as a matter of course.  The Pentium problem is a *bug*.  It's
    repeatable and can potentially break programs that rely on it
    performing up to specification.
    
    As for other bugs in previous systems, a manufacturer has an obligation
    to make good when it doesn't deliver on its promises.  Otherwise, it
    is appropriate for the market to adjust.  In this situation, if
    customers perceive that they have buggy processors it will reflect on
    the business they do.  Some will go back to 486 systems.  Some will
    abandon PCs altogether.  Some will invest in software or other changes 
    to verify the accuracy of their Pentiums.  Some will ignore the issue,
    but will still feel uneasy about when they might get bit by the bug.
    
    In the future, P6 will probably be greeted with increased skepticism.
    486 systems may hold more value than expected.  "Bug-free" Pentiums
    will probably have higher value than current releases.  More people
    will want to upgrade to the bug-free Pentiums, so there may be an
    opportunity there.
    
    Of greater concern to me is the upgrade path.  Seems like buying
    upgradability with a Pentium system is pretty much a wash.  Folks
    already got burned with promises of upgradability in 386 and 486
    systems.  I expect similar burnings to occur with Pentiums (because of
    voltage differences, cooling requirements, socket differences, costs
    and so forth).
    
    I think this presents a great opportunity for Digital and Alpha.  But,
    I don't think Digital has yet figured out how to really take advantage
    of it from a marketing point of view.  
    
    One way Digital might be able to take advantage of this might be to
    market some sort of incentive to migrate to Alpha for our Pentium 
    customers concerned about the Pentium bug.  "Why wait for a better P5 or
    P6 when you can have true 64-bit, 245 MHz processing now?  For a
    limited time, Digital is offering a special upgrade offer for its
    Pentium customers ..."
    
    Steve

    ...we're all waiting to see the hastily scrawled sign in the
    shop window propped up next to the Pentium system...
    
    ...Downgradable to a 486

>    Sorry to sound stupid, but what is this FDIV Bug, and how does it
>    manifest itself?
    
    
Try the following in Excel
    
    5505001/294911
    
    If you have the bug you will get 18.66600093 instead of 18.66651972981
    
    Try also 4195835/3145727

    RE:  .56
    
    Steve,
    
    Thanx for the clarification.

Hmmm ... my 386 yields:

5505001/294911 = 18.666651972968

Not that I care all that much ... or, at least I don't THINK I care but,
then again, my checkbook doesn't always balance all that well, either ...

mark

    Here is the easiest way to tell if your Pentium plays fast and loose
    with floating point math.
    
    1) Select the Calculator from the Accessories Group of Windows.
                                 
    2) Enter the following:
    				4195835 - 4195835 / 3145727 * 3145727
    
    3) As a quick bit of study will tell you, this equation should produce
    a zero result. However, in the Brave New World of Intel Math you will
    come up with 256. I have tried this procedure and it has produced the
    256 result on every Pentium on which it was tried.
    
    In my opinion, this issue is much more serious than Intel has
    acknowledged. I suspect that if Intel is not more forthcoming in their
    response, they will be looking at a class action lawsuit in the near
    future.
    
    Russ
    (Proud owner of an antiquated, yet mathematically correct 486)
    
    				

    Intel has released their analysis on the bug via WWW:
    
    
http://www.intel.com/product/pentium/fpushort.html
    
    It is from 1 December. Since their analysis that the average
    user may expect to see this bug once in every 27000 years
    doesn't go down too well with the results of the previous 
    reply I would expect the report to be updated soon...
    (like perhaps twice in every 27000 years? :-)
    
    re roelof

    re .-1
    
    But if INTEL sells 1 million Pentiums a year, then the expected 
    number of wrong answers would be about 40/year. (10E6/27000). 
    Proportionally more for higher volumes. And more likely in 
    floating-point intensive operations like aircraft or nuclear
    reactor design.

    What I don't understand is why everyone is skirting the real issue! 
    All I want to know is: will I win more solitaire games on an old
    Pentium or the new improved model? ;^)

    Fran

re: "The average user will see the error once every 27000 years"

Guess I'm not an average user then - I've seen it about a couple
of dozen times so far this week, the most recent time being
10 (9.999978) seconds ago when I read .62

    re: "The average user will see the error once every 27000 years"
    
    sure - if we just do math on random numbers!  I suspect that when
    you've got the problem, you've got it bad.  it isn't like you can just
    rerun the program at the answer will be right the next time.  I hope
    that intel payroll is running on intel machines instead of axp
    machines!

    An absolutely fascinating overview of the whole Pentium affair
    is available at:
    
    	http://www.mathworks.com/Pentium/README.html
    
    It consists of a series of the most important postings on
    the subject on the Internet. The current status report (5
    December) indicates that a team of Intel and some of the
    people who have provided the major contributions to the
    subject on the Internet are now all working together to
    provide a workaround.
    
    It appears that Intel has adopted an "if you can't beat them
    then join them attitude" and is apparently contacting and
    contracting various people on the Internet who have brought in
    the most important (and brilliant) contributions.
    
    The work around itself looks pretty impressive.
    
    Fascinating stuff. History in the making. Not just the
    technical stuff but even more the underlying sociological phenomenon
    of a large computer company working hand in hand with the
    Internet community to solve the problem.
    
    Intel appears to have caught on to the right approach and now may well 
    end up coming out of this affair stronger than when they went in.
    
    One 100% guaranteed prediction: Intel will be putting serious
    resouces into strengthening and improving its Internet presence
    from now on...
    
    re roelof

    Its obviously all smoke if Intel are trying to suggest that an
    "Average" user would even live to be 27000 !  To my way of thinking,
    thats a pretty extraordinary user.

INTEL STOCK SPLIT ANNOUNCED

Santa Clara, CA, 12/2/94

Intel  (NASDAQ: INTC) today announced a 3 for 1.99994562416 stock split
effective Jan 5, 1995, for stockholders of record as of Dec 9, 1994.

Although analysts were surprised about the strange ratio in the stock split,
an Intel spokesman stated that "That's just the way the math worked out!"

Intel also filed a motion with the SEC requesting that it be allowed to
publish it's financial reports to only 1 or 2 significant digits stating that:
"There are significant efficiencies to be gained, both in the preparation and
printing of financial reports.  Just as taxpayers can choose to file returns
using the whole dollar method, we feel we can get financial reports out much
faster if we don't have to rerun all our spreadsheets through a PowerPC to
verify them. Besides, most investors only care about the first 2 significant
digits anyway!"

In related news, Microsoft Corporation  (NASDAQ: MSFT) announced that its
chairman, Bill Gates, had filed for personal bankruptcy after discovering
that his personal net worth had been overstated by approximately $8 billion due
to a undisclosed computer glitch.

	... jokes going around the Internet in this week's issue.

    I have to comment on our business response to the Pentium bug.
    That same Internet which is yielding a bumper crop of Intel jokes also
    contained the comment by one Digital customer that our policy of
    sending DECpc customers to Intel for a replacement Pentium chip stands
    in contrast to Compaq, which is replacing their Pentium chips free of
    charge.  The customer's comment was that Compaq stands behind its
    product and Digital does not.
    
    I hope that we are preparing a policy that appears to position us right
    behind our product.  I hope it is announced quickly.

    Digital's policy is that we're telling them to call Intel's 800 #.

    
    I remember a program where we tried to get into the VAR Business....
    applicationDEC433MP and were quite upset when the vars that resold our
    equipment called Digital for service and support.......It's probably
    these same people that made the bonehead decision to step outa the
    way of responsibility and tell the Customers that bought OUR stuff
    to call Intel to solve OUR problems.  Management at it's best.
    Why can't someone figure out that this is the epitomy of
    irresponsibility at it's best. FIRE the bonehead, and move on!
    
    Hey digital, it may say INTEL INSIDE, but it's DIGITAL OUTSIDE, and
    that 'used' to mean something.
    
    this is a sad commentary.
    
    chet

    And in Europe, we're telling them to call a number in UK. I don't think
    they have multilingual operators, and not everyone in Europe speaks
    English...
    
    Read yesterday in a local Munich newspaper:
    
    How many players does Intel's soccer team have?
    
    You guessed it...
    
    10.9999874
    

    Great 
    
    Dear Crysler service rep 
    
    My '92 Caravan's 3.0 has a bad knock in the rear three cylinders. I've
    heard that this is a known problem causes by the sleeve disign of
    the piston and that there is a replacement that does not exhibit these
    problems. When can I schedule my Caravan for service and how long
    should it take.
    
    Brian V
    
    
    Brian 
    	Yes this is a known problem and yes replacement parts are available
    that fix this. However our warranty does not extend to the parts that
    we source from other manufacturers .... so you will have to contact
    Mitsubisi and see if they can do anything for you.
    	I would like to express my simpathy for your problem and reassure 
    you that Crysler stands behind it's products 100 % ....so if you ever
    have a problem with the bend coming out of a door skin  please let
    us know and we'll look after you right away.
    
    Regards
    
    Fred  

    You know, I'm looking at the warranty card for the Digital PC in my
    office.  It reads, in part:
    
    	Digital products are warranted against defects in workmanship and
    	material...  Digital will repair or replace any defective Digital
    	product...
    
    Now, what is a "Digital product"?  In the accompanying warranty table,
    CPUs, monitors, and printers are listed.  We don't make the CPU chips,
    but then we don't always make the monitors or printers either, do we?
    I happen to know that Sony makes a lot of CD-ROM drives, but CD-ROM
    drives are not mentioned at all, and thus I can presume that Digital,
    like Apple, warranties them as part of the CPU.
    
    Of course, I must also report that the warranty further states:
    
    	Digital does not warrant the operation or execution of any product
    	will be uninterrupted or error free.
    
    Maybe that's the loophole 8^(

    Let me expand my point a little.  The Digital PCs we market with Intel
    CPUs are, like those of our competitors, assembled from components
    built by others.  We might very well be selling a system composed of:
    
    	CPU by Intel
    	other chips by Intel, Motorola, Sony, TI, Mitsubishi, IBM, etc.
    	CD-ROM drive by Sony
    	diskette drive by Sony
    	keyboard by Honeywell
    	monitor by Sony
    	hard disk by Seagate
    	
    	MS-DOS and Windows by Microsoft
    	documentation by an outsourcing vendor
    
    (I'm sure I have many of these manufacturers wrong, but you get the
    point.)
    
    Digital includes a warranty with this product.  But if we do not stand
    behind the CPU because we didn't make it, what exactly is there to stand
    behind?  The enclosure?  The packaging?  The nameplate?

    
>    Digital includes a warranty with this product.  But if we do not stand
>    behind the CPU because we didn't make it, what exactly is there to stand
>    behind?
    
    Personally, I'ld say that large metal filing cabinet over by the
    corner :-)

    
    <sigh> 
    
    No amount of advertizing will undo the ill-will this will create. 
    jc
    

    So WHAT EXACTLY is our position?  What is our response when a customer
    asks about a replacement chip?
    
    I got such a call yesterday; the customer said one of the XL590 systems
    I sold him flunked the math test and he wanted to know how Digital
    was going to address this.
    
    If we are to tell customers to contact Intel (shudder), who do they
    call?

    I would have thought CS would have taken care of this as it comes under
    the CS FCO category..... we build the cost of such things into the
    price of the warranty elements of the equipment. Ofcourse things may
    have changed.

Re: .81

According to http://www.intel.com/about-intel/press/andy-msg.html :

     _________________________________________________________________
   
       ANDY GROVE'S INTERNET MESSAGE TO SCIENTIFIC FLOATING POINT USERS
                                       
   This is Andy Grove, president of Intel. I'd like to comment a bit on
   the conversations that have been taking place on the Internet.
   
   First of all, I am truly sorry for the anxiety created among you by
   our floating point issue. I read thru some of the postings and it's
   clear that many of you have done a lot of work around it and that some
   of you are very angry at us.
   
   Let me give you my perspective on what has happened here.
   
   The Pentium processor was introduced into the market in May of '93
   after the most extensive testing program we at Intel have ever
   embarked on. Because this chip is three times as complex as the 486,
   and because it includes a number of improved floating point
   algorithms, we geared up to do an array of tests, validation, and
   verification that far exceeded anything we had ever done. So did many
   of our OEM customers. We held the introduction of the chip several
   months in order to give them more time to check out the chip and their
   systems. We worked extensively with many software companies to this
   end as well.
   
   We were very pleased with the result. We ramped the processor faster
   than any other in our history and encountered no significant problems
   in the user community. Not that the chip was perfect; no chip ever is.
   From time to time, we gathered up what problems we found and put into
   production a new "stepping" -- a new set of masks that incorporated
   whatever we corrected. Stepping N was better than stepping N minus 1,
   which was better than stepping N minus 2. After almost 25 years in the
   microprocessor business, I have come to the conclusion that no
   microprocessor is ever perfect; they just come closer to perfection
   with each stepping. In the life of a typical microprocessor, we go
   thru half a dozen or more such steppings.
   
   Then, in the summer of '94, in the process of further testing (which
   continued thru all this time and continues today), we came upon the
   floating point error. We were puzzled as to why neither we nor anyone
   else had encountered this earlier. We started a separate project,
   including mathematicians and scientists who work for us in areas other
   than the Pentium processor group to examine the nature of the problem
   and its impact.
   
   This group concluded after months of work that (1) an error is only
   likely to occur at a frequency of the order of once in nine billion
   random floating point divides, and that (2) this many divides in all
   the programs they evaluated (which included many scientific programs)
   would require elapsed times of use that would be longer than the mean
   time to failure of the physical computer subsystems. In other words,
   the error rate a user might see due to the floating point problem
   would be swamped by other known computer failure mechanisms. This
   explained why nobody -- not us, not our OEM customers, not the
   software vendors we worked with and not the many individual users --
   had run into it.
   
   As some of you may recall, we had encountered thornier problems with
   early versions of the 386 and 486, so we breathed a sigh of relief
   that with the Pentium processor we had found what turned out to be a
   problem of far lesser magnitude. We then incorporated the fix into the
   next stepping of both the 60 and 66 and the 75/90/100 MHz Pentium
   processor along with whatever else we were correcting in that next
   stepping.
   
   Then, last month Professor Nicely posted his observations about this
   problem and the hubbub started. Interestingly, I understand from press
   reports that Prof. Nicely was attempting to show that Pentium-based
   computers can do the jobs of big time supercomputers in numbers
   analyses. Many of you who posted comments are evidently also involved
   in pretty heavy duty mathematical work.
   
   That gets us to the present time and what we do about all this.
   
   We would like to find all users of the Pentium processor who are
   engaged in work involving heavy duty scientific/floating point
   calculations and resolve their problem in the most appropriate fashion
   including, if necessary, by replacing their chips with new ones. We
   don't know how to set precise rules on this so we decided to do it
   thru individual discussions between each of you and a technically
   trained Intel person. We set up 800# lines for that purpose. It is
   going to take us time to work through the calls we are getting, but we
   will work thru them. I would like to ask for your patience here.
   
   Meanwhile, please don't be concerned that the passing of time will
   deprive you of the opportunity to get your problem resolved -- we will
   stand behind these chips for the life of your computer.
   
   Sorry to be so long-winded -- and again please accept my apologies for
   the situation. We appreciate your interest in the Pentium processor,
   and we remain dedicated to bringing it as close to perfection as
   possible.
   
   I will monitor your communications in the future -- forgive me if I
   can't answer each of you individually.
   
   
     _________________________________________________________________
   
   The 800 number referenced in the above message posted by Andy Grove is
   800-628-8686. For International customers, the number is
   916-356-3551.
     _________________________________________________________________
   
   Last modified: 11/29/94
   
   [Intel] 
    [email protected]
    
   Tell us what you think!
   Copyright (c) 1994, Intel Corporation. All rights reserved. 

    Rather embarrassing wouldn't you say?
    Especially now that we're telling the world that we will do whatever
    it takes.

    
    If I were running this ship, I's order a bunch of good Pentiums from
    Intel, swap them in with no questions and no cost for any customer who
    complained, then deliver the defictive units back to Intel and demand
    my money back.
    

re .84

No, you're missing the point.  We'll do Whatever It Takes
to avoid replacing your CPU chip.

    Well - in rereading the Whatever It Takes copy - I can't see where
    we claim to stand behind anything we sell.
    
    Maybe it would more appropriate to adjust the compaign to say
    Wherever It Drops

    Sorry - it's getting late and I'm not thinking clearly.
    
    Make that Whenever It Works

    re .85: The problem is, there ain't no good Pentiums to buy (yes, I'm
    sure you can _order_ some).
    
    According to discussions in various newsgroups, notesfiles, trade
    magazines, what-have-you, it may take some time before the fixed
    version actualy hits the market.
    

    Then Compaq, which has already announced it will switch chips, is
    getting favorable publicity *without doing anything*!
    
    Why do we have to garner bad press for not doing anything?
    Why aren't we that smart as Compaq?

    re: .89
    
    Internet folks are claiming to be selling new boards with the new 
    "bug-free" Pentiums now.  And, some folks are already asking for
    "buggy" Pentiums at a reduced price, some predicting that prices will
    drop on these.
    
    My guess?  Most PC-literate folks are already used to rebooting, 
    reworking, tweeking and so forth when things don't go right.
    If/when they do hit the bug they probably figure it won't take much to
    work around it.  In essence, they *know* that even a buggy Pentium is
    better than a 486 for what they want to do.  So, the price for Pentiums
    will not drop as low as these folks figure because they will still have
    high demand for the chip, buggy or not.
    
    For others less "literate," they will probably push for "bug-free"
    units, but (aside from the check that has been widely circulated) will
    be hard pressed to show a real application where they are affected by
    the bug.  For them, it's an aesthetic thing.  As things are going, they
    probably won't get a "free" upgrade and will probably hold onto what
    they have.  The result for them will be mistrust towards all involved
    with selling them the machine (unless a free upgrade was done a la
    IBM).  But, even then they will probably keep demand for Pentium's up.
    Even if IBM swallows the cost of the Pentiums they replace, I think
    they will come out ahead.  They probably realize that they can still
    use them internally with no big problems.  If they get too many, they
    can sell them outside.  I think there will be buyers and that they will
    be able to recover a significant portion of their costs.
    
    Man, if ever there was an opportunity for Digital to prove it does
    Whatever It Takes, this was it.  I'm really disappointed.  I know it's
    a gamble to take in the cost of the chips, but surely much of the cost
    could have been recovered, if only through EPP or something.
    
    Steve

From: "wirt (Richard Wirt)" <[email protected]>
Newsgroups: sci.math.num-analysis
Subject: Software workaround for FDIV
Date: 8 Dec 1994 02:38:51 GMT
Organization: Intel

Intel is actively working with leading members of the software 
community to define and implement a uniform, efficient software 
workaround for the floating point divide flaw on the current version
 of the Pentium (TM) processor.

To create this patch we are have formed an informal industry working 
group -- including Cleve Moler of Mathworks, Tim Coe of Vitesse 
Semiconductor, Peter Tang of Argonne National Laboratories and Terje 
Mathisen of Norsk Hydro -- to work with Intel's engineers.

The patch will include an FDIV workaround based on identifying the 
divisor and dividend for regions that can yield imprecise results. 
This approach will provide the best solution with the least 
performance impact to the end user.

Many of you have been concerned about the transcendental instructions 
that use FDIV. Sine, cosine and the exponentials have been proven not 
to be impacted by the floating point flaw. We will include a library 
for tangent, arc-tangent and the remainder, all of which use the FDIV 
operation.The proof for the log functions' not being impacted by the 
flaw is still being pursued.

Intel is now working with compiler vendors to incorporate the patch 
into their compilers and compiler libraries. After we have completed 
validation of the patch, and the major compiler vendors have completed 
validation with their test suites, we are committed to posting the 
workaround on the Intel WWW server (http://www.intel.com). We expect 
to have this posted by the end of 1994.

Dr. Richard Wirt
Intel Fellow
Director, Software Technology Laboratory

The reaction of Intel to the FDIV bug reminds of the Perrier affair a couple of
years back:

In a few (literally) bottles of Perrier Table water traces of cleaning fluids
were found.
Perrier's reaction:
They withdrew every bottle on the market worldwide at their own expense, told the
world about it and came out of this stronger than ever (the competition even com-
plained about this "marketing stunt").

Intel's reaction transformed:

tell the world that their tastes are so bad tey'll never know the difference and
besides, a few traces of Benzene won't kill you. Well.. if you can prove to us
that you're dying you can mail us the bottle and we'll think about a replacement.

Guess what that reaction would have done to Perrier's image...

But nobody (with the exception of Compaq, maybe) has taken this lesson to heart..

Who was it that said "a mistake you make can still be productive if you learn
something from it and don't make the same mistake again !" ???

my $.02, Martin

	>>>besides, a few traces of Benzene won't kill you.
    
    	Martin, I must take issue with this one small detail.  Benzine is a
    known carcigenic substance with no known safe limit!
    
    	Bezine is also added to all unleaded and super unleaded petrol at
    about 2 pints per 10 gallons - a fact that is causing some increasing
    outcry on the right side of the pond!!!
    
    				Malcolm.

Malcolm,

that's precisely the point !!!

Martin

    ><<< Note 3340.96 by GNPIKE::SMITH "Peter H. Smith,297-6345,MR04-2
    C3,Digital Co
    
    Gosh Peter, we closed MRO4 over a month ago.  Didn't you get the
    notice?  :-)

Maybe he's hanging around hoping for good investment advice.

    Intel stock was down by 4 few minutes ago. It appears that IBM has 
    announced that it is halting the shipments of Pentium based systems,
    since the probelm is more extensive than what was admited by Intel..
     

  >  since the probelm is more extensive than what was admited by Intel..
    
    My guess is that the real reason they're doing this is to give a much 
    needed boost to the PowerPC.
    
    Bruce

    
    Has anybody seen a real impact assessment of the problem ?

    I have read some RISK mails stating that :

    - there is a problem with double precision floating point
    - there is a problems with single precision fp
    - code compiled on Pentium may fail even on 486/386, the example given
    	was probably not what vast majority of code does
    - there is an integer arithmetic example in this stream that shows the
      problem

    What do we tell our customers ?

    Another possibly interesting point.

    Does this bug define a transformation or a function ? Is it reversible
    or symmetric. Lets say you encrypt/compress something and some of the 
    values were incorrectly calculated. Can it be decrypted/decompressed ? 

    			w

    
     Another shot at the PowerPC, since it has been quiet lately. So now
    IBM has po'd INTEL. Hmmmmm, my thinking says good. Let us now approach
    INTEL with ALPHA and say, want to help us make some new rules. We have
    the chip, you have the business. Together we change the game and the
    rules. Otherwise everyone just ducks, and the chips fly with the same
    old game as before.
    
    -IMHO
    Mike Z.

    Great, a software fix.  That means I have to upgrade all of my software
    again -- or at least the stuff I really use.  I bet the stuff will
    all require Windows95 by that time too.
    
    My guess is that IBM said "We want 50000 fixed pentium chips to fix
    our customers."  And Intel said "Have them talk to our phone lines and
    we'll fix the ones that 'need it'"  And IBM said "Marketing opportunity
    for PowerPC!!!"
    
    ed

    While I have no doubt that Intel will remain the biggest player in the 
    market for the remainder of the decade, I think the days of 75%(or
    whatever the number is) of the microprocessor market will be coming to
    an end.  IBM can make all the 486 they need and they can start to
    sell the Cyrix M1 in the near future, so they no longer need Intel.
    Compaq has has AMD as a second(or first) source for 486's and AMD's K5
    will be available in CY95. Digital's new Venturis line uses AMD 486
    processors. 

    -Bruce   

    IBM has featured this as the lead story on their Web Server. Released
    12 December 1994.
    
See http://www.ibm.com/Features/pentium.html

Summary: 

IBM Research focused on the likelihood of error on the Pentium chip 
in everyday floating point division activities. Intel has analyzed 
the probability of making an error based on the assumption that any 
possible 64 bit pattern is equally likely to occur in both the 
numerator and the denominator. If that were the case, then the
chances of the error would be 1 in 9 billion. They also estimate 
that an average spreadsheet user will perform 1,000 floating point 
division per day. Based on these assumptions, Intel estimates that 
an error will be encountered only once in 9 million days (or 
once in about 27,000 years). 

Our analysis shows that the chances of an error occurring are 
significantly greater when we perform simulations of the types 
of calculations performed by financial spreadsheet users, because, 
in this case, all bit patterns are not equally probable. 

Probability Tests: 

We have analyzed a Pentium chip in order to understand the sources of 
errors and have found that in order for an error to occur, both the 
numerator and denominator must have certain "bad" bit patterns, as 
described below. 

First, for the denominator to be "at risk", that is, capable of producing 
an error with certain numerators, it must contain a long string of 
consecutive 1's in its binary representation. Although such numbers 
represent only a very small fraction of all possible numbers, they do 
occur much more frequently when denominators are created by adding, 
subtracting, multiplying or dividing simple numbers. For example, the 
number 3.0 represented exactly, does not have that pattern, but the 
result of the computation 4.1-1.1 does have that pattern.

How many denominators produced in this fashion can be "at risk" that is, 
capable of producing an error for certain numerators? When we randomly 
added or subtracted ten random numbers having a single digit dollar
amount and two digit in cents, for example, $4.57, then one out of every 
300 of the results was "at risk" and hence capable of producing an error. 
If we repeated the test with numbers having two digit dollar amounts 
and two digits in cents, then one out of every 2,000 could cause an error. 
If the denominator was calculated by dividing two numbers having one digit 
to the left and one to the right of the decimal point, then approximately
one in every 200 could cause an error. 

For simplicity, suppose that one of every 1000 denominators produced by 
some calculations was "at risk." 

Now, suppose we have created a bad denominator. What is the chance of now 
encountering a bad numerator, which will produce an error? It depends on 
the actual value of the "at risk" denominator, but based on our tests,
a conservative estimate would be that only one out of every 100,000 
numerators causes a problem. 

Finally, when we combine the chances of a bad numerator and the chances 
of a bad denominator, the result is that one out of every 100 million 
divisions will give a bad result. Our conclusion is vastly different 
from Intel's. 

Frequency Tests: 

We also questioned Intel's analysis and assumption that spreadsheet 
users will only perform 1,000 divides in a day. Tests run independently 
suggest that a spreadsheet user (Lotus 1-2-3) does about 5,000 divides 
every second when he is calculating his spreadsheet. Even if he does this 
for only 15 minutes a day, he will perform 4.2 million divides in a day, 
and according to our probability findings, on average, a computer could 
make a mistake every 24 days. Hypothetically, if 100,000 Pentium customers 
were doing 15 minutes of calculations every day, we could expect 4,000 
mistakes to occur each day. 

Conclusion: 

The Pentium processor does make errors on floating point divisions 
when both the numerator and denominator of the division have certain 
characteristics. Our study is an analysis based on probabilities and 
chances. In reality, a user could face either significantly more errors 
or no errors at all. If an error occurs, it will first appear in the 
fifth or higher significant digit and it may have no effect or it may 
have catastrophic effects. 

Additional Technical Detail: 

Some Experiments on Pentium Using Decimal Numbers 

According to an Intel white paper, if you were to choose a random binary 
bit pattern for numerator and the denominator, the probability of error 
in divide is about 1 in 9 billion. The error occurs when certain 
divisors (termed "at risk" or bad) are divided into certain numerators. 
In order for the error to occur, our belief is that divisors must lie 
in a certain range. For each such denominator, there is a range of 
numerator values which produce an incorrect result. 

An example of affected numbers is the decimal constants we hardwire 
in our programs. For example, if converting from months to years and 
we are interested in 7-8 decimal digits of accuracy, then we can hard 
wire a constant to convert from months to years. 

 
        alpha = 1/12 = .083333333
 

Let us construct a hypothetical example. We have contracted a job which 
is expected to last 22.5 months. The total value of the contract is 
$96000. From this, tax at the rate of 14 and 2/3 percent rate has to 
be deducted. The taxing authority has defined 14 and 2/3 percent to 
be 14.66667. We want to calculate the net take at a per annum basis. 
We do the following calculations. 

 
      Tax = 96000*.1466667 =  14080.0032

 Net take home money = 96000 - 14080.0032 = 81919.9968
 The number of years in 22.5 months = 22.5*.083333333
                                    = 1.8749999925 years
 
 Net take home money per annum =  81919.9968/1.874999925
 
                               =  $43690.6667
 

Most machines give the above answer which satisfies the desired 7-8 
digit accuracy criterion. On Pentium, the answer is $43690.53, which 
has only 5 correct digits. 

In this example, both numerator and denominator are bad numbers. They 
are both near some simple integer boundary in their binary presentation 
and as you rightly observed, these numbers occur in real world at a much
higher frequency compared to the totally random bit pattern hypothesis. 

Probabilistic Analysis 

We are addressing the question of how likely it is to have a bad divisor. 
On Pentium, a bad divisor belongs to one of the five bad table entries 
characterized by 1.0001, 1.0100, 1.0111, 1.1010, and 1.1101, followed by a
string of 1's in the mantissa. 

We have found that if the string of 1's is of length 20 or so, then it 
is a bad divisor. Given a bad divisor, the probability of making an 
error in the division increases dramatically, compared to the 1 in 9 
billion figure quoted by Intel. 

We did some simple experiments using decimal numbers and the findings 
are reported below. We counted only those bad divisors which belong to 
one of the above five table values, followed by a string of 32 1's. 
Intel people argue that all binary patterns are equally likely. If that 
was really the case, the probability of finding a bad divisor, as defined 
above, will be 5/(2**36) or about one in 13 billion random divisors. 
However, we are finding the probabilities to be much higher. 

Addition/Subtraction of Decimal Numbers 

In this experiment, we randomly added or subtracted, 10 uniformly 
distributed random numbers having one or two decimal digits (as in 
dollars and cents) and then we examined the result for the above 
binary patterns. Here are the results for two cases. In the first case, 
we chose only one digit to the left of decimal (as in $3.47) and
in the second case, we chose two digits to the left of the decimal 
(as in $29.56). All the digits were chosen randomly with uniform 
probability. In the third case, we chose one digit to the right of 
the decimal point and two digits to the left. The results below give 
the number of times the result of this experiment has the bit
pattern corresponding to a bad divisor. 

 
 Case 1 (one digit to the left, two to the right)   ---   188 out of 100,000
 Case 2 (two digits to the left, two to the right)  ---    45 out of 100,000
 Case 3 (two digits to the left, one to the right)  ---   356 out of 100,000

Clearly, these probabilities are much higher than those obtained with the 
random bit pattern hypothesis. 

Division Of Two Decimal Numbers: 

These experiments were conducted through exhaustive tests on all possible 
digits patterns. Here (a.b)/(c.d) represents division of a two digit (one 
to the left of the decimal point and one to the right of the decimal point)
number by another two digit number. 

  
     (a.b)/(c.d)       -     44 out of 10,000
     (0.ab)/(0.cd)     -     27 out of 10,000
     (a.bc)/(d.ef)     -    344 out of 1,000,000
     (ab.c)/(de.f)     -    422 out of 1,000,000

Multiplication of Two Numbers 

Here we are multiplying a decimal number by another number which was 
computed as a reciprocal of another decimal number as in scaling by a 
constant. 

  
     (a.b)  * (1/(c.d))       -    37 out of 10,000
     (a.bc) * (1/(d.e))       -   139 out of 100,000
     (a.bc) * (1/(d.ef))      -   434 out of 1,000,000

To summarize, for the decimal calculations of the type given above, the 
probability of having a result which falls into the category of being a 
bad divisor is rather high. It appears to be somewhere between 1 in 3000 
to 1 in 250. Let us say that it is of the order of 1 in 1000. 

Furthermore, if the rounding mode corresponds to truncate, the probability 
of arriving at bad divisors increases significantly. 

The Dependency on Numerator 

Given a bad divisor, the divide error occurs for some range of values 
of the denominator. If we were to take a totally random bit pattern for 
the denominator, the probability of error appears to be of the order one 
in 100,000. This is a first cut rough estimate and probably could be 
improved. It appears that probabilities are different for different table 
values. The table corresponding to '1.0001' seems to have the most error. 
For numerator also, there are bands of values where the error is much more 
likely. Again these bands are more prominent near whole numbers. For 
example. if we were using (19.4 - 10.4) = '9' as a divisor (a bad one), 
and you picked a random value between 6 and 6.01, as the numerator then 
the chance of error increases to about one in 1000. 

For the purpose of our simplistic analysis, we will use the figure of 1 
in 100,000 for a bad numerator. This assumes that we are picking up a 
random numerator. Using the value of 1 in 1000 as the probability for a bad
divisor, the overall probability for a 'typical' divide being incorrect 
seems to be of the order of 1 in 100 millions. This is about two orders of 
magnitude higher compared to the Intel estimate of 1 in 9 billion. 


Probability of a Divide Instruction 

Let us assume that a Pentium operating at 90 MHz does an op in 1.2 cycles 
on the average. That will give about 75 Million ops per second of actual 
compute time. We will use a figure of 1 divide per 16,000 instructions,
even though many estimates suggest a much higher frequency of divide. 

Thus using this conservative estimate of one divide per 16,000 instructions, 
    we come up at about 4687 divides per second. Let us further assume 
    that a typical spread-sheet user does only about 15 minutes of actual 
    intensive computing per day. Then, he is 
likely to do 4687*900 = 4.2 million divides per day. Assuming an
error rate of 1 in 100 million, it will take about 24 days for an error 
to occur for an individual user. 

Combine this with the fact that there are millions of PENTIUM users 
worldwide, we quickly come to the conclusion that on a typical day a 
large number of people are making mistakes in their computation without
realizing it. 

IBM Corporation
[email protected]

    If any of you have the opportunity to escalate this issue
    (today) please do so. I have personally already expressed worries
    exactly 1 week ago that Digital is underestimating the severity
    of the situation (GIADEV::DECSTATION 5305.6) and sent mails at
    the time to the people formulating/distributing Digitals'
    messaging.
    
    My contention at the time was that a more proactive Digital reaction
    could save us all from having to go into damage control mode.
    
    I believe it fair to say that with the release of the IBM study
    yesterday we have now in fact entered damage control mode.
    
    re roelof

    How many Pentiums (Pentia?) have we sold?
    

It's interesting to compare IBM's calm analysis of
the problem with Intel's "sincere" assurances that, really,
we won't notice anything wrong.  Score one for Big Blue here.

    Time Magazines Daily News report: "BIG BLUE CHEWS UP INTEL CHIP"
    
    See http://www.timeinc.com/time/daily/time/latest.html

    This morning on the CNN business news IBM was chastised for overstating
    the severity of the error, apparently fed by Andy Grove's news
    conference yesterday which all but accused IBM of child abuse.. 
    
    My gut says the truth is somewhere in the middle; Intel is clearly
    waaaay off base when they say that the average spreadsheet user does
    1000 floating divisions a day, or that random bit patterns match the
    distribution of FDIV operands.. but IBM may well be contriving cases
    which overstate the probabilities.. 
    
    It is kind of interesting to watch, though.. and to hypothesize what
    Digital would do in similar circumstances..
    
    ...tom

re: 111
Digital did have a simular problem with the F11 floating point chip set in the
early 80's. A floating point bug was discovered after the chip set had been out
for some time. From my recollections we replaced  ALL floating point chip sets
(possible boards because they were soldered in). I seem to remember the cost of
this to have been around $1 million which back then was note worthy. I may have
the numbers wrong I was a diagnostic engineer and not in marketing or management.

I then was assigned to create a better floating point DVT for the J11 chip set.
The new DVT included a program to generate random floating point
instructions/data and compare the results with a software simulation of the same
instruction/data. This test was run on engineering test system during dedicated
test times and anytime the systems were not being used for other testing. I
don't believe we have had a simular chip problem since then.

See today's Wall Street Journal - page 1 for the story on IBM's halt of
Pentium shipments.
Mark

    Another missed opportunity...
    
    Roelof's right.
    
    Laurie.

    Potentially worse:
    
    WBUR Radio (which broadcasts National Public Radio out of Boston
    University) had a quick blurb at about 8:25am today: "Digital Equipment
    Corpration will continue to ship personal computers with the flawed
    Pentium processor." Sentence 2 was that IBM announced they will stop
    shipping. Sentence 3 was a, um, assertion that Digital says that users
    will only notice the problem in once every 27,000 years. No mention of
    Intel.

    re .115:
    
    Oh, great...
    
    ...tom

    Perhaps the grip of certain of our partners on certain of our body
    parts should be loosened just a tad.
    

    
    
    Intel may be understating the issue, but IBM appears to be overstating 
    it:
    
>We also questioned Intel's analysis and assumption that spreadsheet 
>users will only perform 1,000 divides in a day. Tests run independently 
>suggest that a spreadsheet user (Lotus 1-2-3) does about 5,000 divides 
>every second when he is calculating his spreadsheet. Even if he does this 
>for only 15 minutes a day, he will perform 4.2 million divides in a day, 
>and according to our probability findings, on average, a computer could 
>make a mistake every 24 days. Hypothetically, if 100,000 Pentium customers 
>were doing 15 minutes of calculations every day, we could expect 4,000 
>mistakes to occur each day. 

    This logic appears flawed.  A spreadsheet only performs the calculations
    when the user changes a value.  Then only potentially effected elements 
    of the spreadsheet are recalculated.  Even if all recalculations were
    triggered continually, it will not matter:  the operands would be the
    same (Pentium only fails on certain pathological operands, if the
    operands were OK the first time, they will be OK the second).  
    
    Let's say a typical spreadsheet requires 5,000 divides to calculate
    results (it recalculates in a second).  Changes in data occur when the
    user enters new values.  
    
    Assuming the following:
    
    	5,000 divides for the base flowsheet
    	  500 divides on each update (10% of the above)
    	   15 seconds between updates
    
    The number of new FDIV instructions in a 15 minute session will be:
    
    		 	 5,000		for the initial calculation
    	500*60*15/15 or 30,000		for recalculations
    			------
    			35,000		Total new calculations
    
    A number much less than the 4.2 million divides given by IBM.
    
    I'm not endorsing Digital's apparent decision to direct potentially
    affected customers to Intel, but IBM's analysis appears to me to be 
    sensationalized (not calm as mentioned in a previous note).
    

    It's interesting that IBM's anti-Pentium P.R. seems to be coming
    from headquarters in upstate New York and not the PC group in Boca
    or Raleigh.  Makes you wonder how much of a say their PC group
    had in the whole thing.

    As for as IBM making an opportunity out of this, OS/2 does not yet run
    on the PowerPC chip, so what do they offer?  RS/6000 system for your
    desktop?  How about a PowerMAC?
    
    Other than future sales of OS/2 on the PowerPC, how does IBM
    "effectively" take advantage of this?  I do not believe that OS/2 is
    long for this world.
    

re .115

	That wasn't what I heard, a little earlier on WBUR.  I don't remember 
the words, but it made us sound responsible and helpful to our customers.  I'm 
sure I did *not* hear us use Intel's line about 27,000 years.

	IBM's recall is something of a publicity stunt.  Also, Intel happens to 
be a *very* large account of ours, and it behooves us to handle this episode 
professionally and not go ticking them off unnecessarily.

		David

    INFORMATIONWEEK, 12-12-94
    
    >IBM's PowerPC machines were originally scheduled to ship in October,
    >but a dearth of applications software and problems with the version of
    >OS/2 for the PowerPC platform prompted Big Blue to put its new machines
    >on hold until late spring or early summer of 1995.  Shortcomings with
    >multimedia features, such as speech recognition and video technology,
    >also contributed to the delay.
    
    Makes me want to go out and buy one.  I can substitute my hardware
    problem (Intel) for a software problem (OS/2).
    
    Perhaps IBM's harping on Intel is a sign of desperation.
    
    

    Re: .121
    
    Was this a longer story or a short blurb? And when did you hear it?
    I have heard WBUR stories "evolve" slowly over an hour and a half of
    Morning Edition. Perhaps they corrected themselves.

   Dr. Dan is right.  It sounds like we are more interested in protecting
   our relationship with a business partner than we are in satisfying our
   customers.  And at least some of our customers are asking us to do
   something about the Pentium chips we sold them...
   
   I know how I would apply the corporate principle "do the right thing;" I
   would replace the customers' Pentium chips, eat the cost, and apologize
   for any inconvenience.  How do I apply the principle "whatever it
   takes?"

    re. 124
    
    "do the right thing"
    
    We are a long way from completely understanding the full extent of the
    problem with the Pentium.  I do not believe that there is yet a
    definitive definition of the problem.  How big, how small.  I think it
    would border or hysteria and possible financial irresponsibility to
    replace all the Pentium chips that Digital has shipped.

   Anent .125 (SANDERS_J): You may be right that it could be hysterical and
   financially irresponsible to replace our Pentium chips.  Would you tell
   that to a customer who asked for a replacement chip, though?  Would you
   say IBM is being hysterical and financially irresponsible?  After all,
   I'd guess they're shipping ten times as many units, so the impact of
   their action could be ten times as great on them...

    Re .125
    	I think we know enough.  The Chips are designed incorrectly (they
    sometimes fail without showing a failure).  Many examples have been
    given already.  What is so irresponsible about replacing defective
    parts?
    
    Jim Morton

    We should be proactive with our customers BUT we cannot replace the
    chip - the new one isn't out yet (and by all reports, won't be till
    next year sometime).
    
    Alan

To a company the size of IBM, the cost of replacing the chips is trivial.  For
that matter, it is to Digital also.  The "right" thing is to replace the chips,
in my opinion.

Posit that an "average" Pentium chip costs $350.

The trade press quotes that IBM has shipped 50,000 Pentium systems.

The "cost" to replace the chips is $17,500,000.
IBM has annnual revenues above $50,000,000,000.

By stopping shipping Pentia, they lean on Intel to get the fix out faster and
cut the costs later (fewer Pentia to replace later).  It is a brilliant, low 
cost move.

Now, as to Digital, assuming we have sold about as many Pentia as IBM
(remember, most of our systems sold are still 486s), the cost of replacing the
chips is 13% of the money we got from Quantum for our storage business.

In other words, monye should not be the driving factor in this equation.

BobW

Given that two major companies are declaring wildly different estimates of the
risks posed by the Pentium, one would hope that Digital also has some maths geniuses
working out probabilities. It is clear that both IBM and Intel have come up with
estimates that cynics will say (already are saying) suit their respective needs.
Digital has an opportunity to "do the right thing" and publish some figures that
are not naive or doomladen or self-serving, but realistic and balanced and reasoned. 

There must be a lot of people who have read both IBM's and Intel's estimates and 
are more confused now than they were beforehand. As a service to our customers, 
we should be publishing the numbers on which WE are basing our decisions, and 
taking the opportunity to show some integrity and balance and leadership. We are 
touting  ourselves as a major player in the PC market, so we need to support that
position  by declaring our views on this important issue. As it stands, Intel and 
IBM are positioned as the voices that matter. Our voice matters too, or should do if 
we want people to recognise our claim to be in the top ten vendors.

I do hope we have not simply accepted Intel's calculations uncritically, so let us
declare our own views on the matter and help our customers make informed decisions.
This is a golden opportunity to demonstrate that Digital are a major PC player too.
 

    For anybody needing to carry out an indepth analysis I can (strongly)
    recommend Prof Vaughan Pratt's (Stanford CS Theory Division)
    collection of postings on the subject. The postings were put
    on line yesterday at: 
    
    	http://www.mathworks.com/pratt.txt
       
    In a nutshell, his analyses come down far closer to the IBM
    position than Intel's position.
    
    The combined set of postings (around 100K) are too long to 
    include here.
    
    re roelof

From: [email protected] (Peter McGavin)
Newsgroups: comp.sys.intel
Subject: FDIV Myths
Date: 08 Dec 1994 04:14:00 GMT
Organization: Applied Maths, Industrial Research Ltd, NZ.

Skimming through this newsgroup, I see the same fundamental errors
about the FDIV (Floating-point DIVide) flaw being made over and over
again.  This is not helped by newspaper reports and official
statements from Intel making the same or similar mistakes.  Rather
than replying to them all individually, I will correct some of these
myths here.

------------------------------------------------------------------------
Myth: To see the FDIV flaw, enter 2.11 - 2.1 in windows calc (or
14.32 - 14.31, etc).

Answer: No, this shows a bug in windows calc and it has nothing
whatsoever to do with the FDIV flaw.  To see the FDIV flaw, try
4195835 - (4195835 / 3145727) * 3145727    or
5505001 - (5505001 / 294911) * 294911

------------------------------------------------------------------------
Myth: Only 90MHz (or 60MHz or whatever) Pentium chips shipped before
September (or June, or November,...) have the FDIV flaw.

Answer: No, all currently available speeds of Pentium chips are
affected.  It seems that most, if not all, brand-name Pentium machines
are still being shipped with the FDIV flaw.  So far only a handful of
people have reported receiving corrected Pentium chips from Intel, but
it looks as if at least some are shipping at last.  No known 486 chips
have the FDIV flaw.

------------------------------------------------------------------------
Myth: The flaw affects the precision of the result only after the 9th
decimal place.

Answer: No, operands can be scaled so that the error occurs in the
tens place or the millions place or any other place.  It is much
better to consider significant digits.  The largest possible errors
occur in about the 4th or 5th significant digit, but most errors are
much smaller than that.

------------------------------------------------------------------------
Myth: An easy workaround for x/y is to compute x*(1/y) instead.

Answer: No, this does not work in general, e.g, for y=824633702441 or
y=12884897291.  The first errors discovered were all of the form 1/y.

------------------------------------------------------------------------
Myth: The FDIV flaw affects only double-precision calculations.

Answer: No, the FDIV flaw affects single-precision, double-precision
and extended-precision floating-point calculations using the FPU, in
all rounding modes.

------------------------------------------------------------------------
Myth: The FDIV flaw affects calculations randomly.

Answer: No, this is only true if your inputs to FDIV are random.
With the same inputs, FDIV always returns the same answer.

------------------------------------------------------------------------
Myth: Approximately 1800 different operand pairs to FDIV produce the
wrong answer.

Answer: No, that is only the number of unique pairs of
single-precision mantissas.  The total number of double-precision
pairs is vastly larger and is probably impossible to count exactly.

------------------------------------------------------------------------
Myth: An error is only likely to occur at a frequency of the order of
once in nine billion random floating point divides.

Answer: This estimate comes from an official message by Andy Grove,
president of Intel.  To put it into perspective, the probability that
you become a road-death statistic tomorrow is very roughly 5000 times
greater than seeing an error in a single random FDIV.  On the other
hand, if your program does nothing but random FDIVs, you should start
seeing errors every hour or so.

Andy Grove's estimate is probably right if the operands are chosen
>from  an idealised uniform distribution over all possible floating
point numbers.  However operands that cause errors are known to be
clustered extremely close to small integers and other commonly used
constants.  Also, numbers used in real life are known to be very far
>from  uniform random (e.g, you almost certainly use the number 2.999999
more often than 4.779031).  Therefore the probability of an error in
real life is likely to be somewhat higher than one in 9 billion.

As an extreme case, if every FDIV you do is 4195835 / 3145727, then
every division results in an error.  But using these numbers is a bit
like using the winning numbers of a lottery after you saw the results.

------------------------------------------------------------------------
Myth: I divided 4195835 by 3145727 (or 5505001 by 294911, etc) and got
the right answer, therefore I have a corrected chip (or vice-versa).

Answer: While this might be true, there are several reasons why this
test can fail.  For example, the software you used might not use the
FDIV instruction at all.  This is often the case with mathematical
programs like Maple and Mathematica that mostly do integer arithmetic,
It is also the case with programs compiled to run on FPU-less PCs.  Or
maybe the FPU was locked out with SET NO87=NO87 or SET 87=NO.

Also, people are still posting executable test programs and
spreadsheets with the answer already compiled into them.  Some
compilers are clever enough to do the division at compile-time, either
with FDIV or with fp-emulation.  Such test programs must be recompiled
>from  source code on each target machine.  Otherwise they always give
the same answer as the machine the program was originally compiled on.
If you post a test binary to a news-group, please check it thoroughly,
e.g, by running the same binary on a 486 and/or disassembling and
identifying the FDIV instruction.

------------------------------------------------------------------------
Myth: Intel's MDIAG diagnostic program demonstrates that there is a
flaw in the Pentium's transendental instructions.

Answer: No.  It's true that the Pentium does fail MDIAG's
transcendental test.  It's also true that at least some transcendental
instructions are flawed because of the FDIV flaw (e.g, FPATAN).
However these are not related.

Okay, a bit of speculation here.  MDIAG was probably engineered by
Intel in 80486 days to fail Cyrix and other clone chips, even though
they are IEEE compliant.  Thus MDIAG rejects anything that does not
give exactly same results as a 486.  The Pentium uses new algorithms
for transcendental instructions and finishes up failing Intel's own
MDIAG because of that.

------------------------------------------------------------------------
Myth: Bridges will collapse, satellites will fall out of orbit, power
stations will explode, the world will end,...

Answer: They probably will, but not because of the FDIV flaw, IMHO...

------------------------------------------------------------------------
--
Peter McGavin.   ([email protected])

TO:       Whom it may concern
FROM:     Dr. Thomas R. Nicely
          Professor of Mathematics
          Lynchburg College
          Lynchburg, Virginia 24501-3199 USA
          Phone:    804-522-8374
          Fax:      804-522-8499
          Internet: [email protected]
RE:       Pentium FPU Bug
DATE:     94.12.09.2115 EST


Enumerated below are some questions that have frequently been posed
to me. Each question is followed by my response.

Many of these questions were submitted by Dr. Denis Delbecq of the
Paris based computer periodical "Science et Vie Micro."

Feel free to transmit unmodified copies of this document as you wish.


/*************************************************************/
Q1:  How can a user check a Pentium machine for the presence of the
bug?
/**************************************************************/


Perform Coe's calculation (see Question 5 below).  That is, carry
out the following division problem:

4195835.0/3145727.0 = 1.333 820 449 136 241 00  (Correct value)
4195835.0/3145727.0 = 1.333 739 068 902 037 59  (Flawed Pentium)

The division can be done in BASIC, in a spreadsheet (such as
Quattro Pro, Excel, or Microsoft Works), in the Microsoft Windows
calculator, or in some other programming language such as Pascal,
C, or Fortran.

Make sure that the FPU has not been disabled (this usually has to
be done intentionally through some specific action).


/*************************************************************/
Q2:  Could you summarize how you discovered the problem?  Were you
doing research calculations or were you studying the problem of
accuracy with computers?
/**************************************************************/


RESPONSE:  I was pursuing a research project in an area of pure
mathematics called computational number theory.  Specifically, I
have written a code which enumerates the primes, twin primes, prime
triplets, and prime quadruplets for all positive integers up to an
extremely large limit (currently to about 6e12).  The totals are
written to a file at intervals of 1e9.  Also computed are the sums
of the reciprocals of the twin primes, the triplets, and the
quadruplets; each of these can be proved to converge to a limit,
but the limit of the sum of the reciprocals of the twin primes is
known imprecisely, and the others have not been previously
computed.  My intent is to publish the results in a research
journal at such time as I have carried the computation to an
extremely large limit (perhaps 20e12) and confirmed the results.

The code is written so that the computation can be distributed over
a large  number of independent systems, with the final results
synthesized upon completion.  The calculation has run for over a
year simultaneously on half a dozen systems; most are 486s, but one
Pentium was added in March, 1994.

Simultaneously with the calculation of the unknown quantities, a
number of checks are maintained by calculating previously published
values (such as pi(x), the number of primes <= x).  The reciprocal
sums are also computed by two different methods---to 19 digits
using the FPU, and to 26 (later 53) decimal places using arrays of
long integers to effect extended precision (some of the code for
this purpose was modified from code kindly made available by Arjen
Lenstra of Bellcore).

On 13 June 1994, a number of results were reassembled, and I found
that the computed check value for pi(x) disagreed with the
published value.  This led to a long search for logic errors and
sources of reduced precision in my source code (some 3000 lines in
all).  In the process, I found that the Borland C++ 4.02 compiler
was producing erroneous code when compiled in 32-bit mode with
certain optimizations (-Op -Om -Og) enabled.  For some time I
believed this to be the source of my woes.

However, after eliminating this source of error, and rewriting the
code to convert certain floating point calculations from double
precision to long double precision, I found that I was still
encountering an error in the reciprocal sums of the twin primes;
the floating point result differed from the extended precision
result by an amount orders of magnitude in excess of that expected
from normal rounding error accumulation.  Through trial and error
and finally a binary search, the discrepancy was isolated to the
pair of twin primes 824633702441 and 824633702443, which were
producing incorrect floating point reciprocals (the extended
precision reciprocals were also in error, to a different degree,
evidently due to some minor dependency on floating point arithmetic
in Lenstra's original integer arithmetic code).

My first conjecture was that the error was again an artifact of the
Borland compiler, but even completely disabling optimization failed
to eliminate the problem.  Tracing the source of the error was
further  complicated by the fact that on one occasion I tested the
code with the Pentium FPU locked out, and the error was still
present (this never happened again, and was apparently due to my
own failure to properly disable the FPU).  Finally, in desperation,
I ran this portion of the calculation on one of the 486s, rather
than the Pentium.  The error disappeared.

Even at this point, I felt the problem might still be in the PCI
bus on the Pentiums, rather than the CPU.  After all, a number of
Pentium PCI systems had been reported in the trade press as
corrupting data due to faulty design of the interface with the PCI
bus (this was especially true of Intel motherboards using the
Neptune chipset).

The final pieces of the puzzle fell in place during the week of 16-
22 October.  On 17 October I gained access to a second Pentium,
which had a motherboard from a different manufacturer.  The error
was present in this machine as well.  On 18-19 October, I
reproduced the error in a code written in Power Basic, eliminating
the C compiler as a cause.  I reproduced the error in a Quattro Pro
spreadsheet, and also verified that the error disappeared when the
FPU was locked out in real-mode DOS (this is difficult to do in
Windows code or 32-bit code, which I was using for my main
application).  On 21 October, I ran the test code on a 486DX2-66
with a PCI bus; when no error appeared, I felt that the PCI bus had
been eliminated as a cause.  On 22 October, I tested the code on
still a third Pentium on display at Staples, a local office supply
store; this Packard-Bell machine also produced the error.  I was
now certain that the error was in the FPU of the Pentium chip.

On or about 19 October, I contacted tech support at Micron, Inc.,
from whom I purchased my system, but they were unable to provide me
with any information regarding the problem.  On 24 October, I
contacted Intel tech support.  After six days, they still had no
answer to the problem.  On 27 October, I provided a colleague with
a copy of the test code; her husband is an engineer in the nuclear
reactor group at the local firm of Babcock and Wilcox.  Babcock and
Wilcox reported to me on 28 October that their new P90 Gateway
Pentiums all appeared to have the bug.

In the absence of any meaningful response from Intel tech support,
on 30 October I sent e-mail to a number of individuals and
organizations who I felt would have access to many other Pentium
systems, and asked them to check for the problem.  I believe you
are aware of events from that point on.


/**************************************************************/
Q3:  In which fields of mathematics and numerical models could the
FDIV roundoff error reduce significantly confidence in the results?
Many people talk about the formulas that demonstrate the problem.
/***************************************************************/


RESPONSE:  Clearly, computational number theory is one area
affected.  Other areas with the potential for major difficulties
include computations in chaos theory (non-linear dynamics), linear
programming or finite element analysis (where ill-conditioned
matrices may be involved), and areas requiring numerical solution
of differential equations by iterative methods (if high precision
is required in the extrapolated result, as in orbital dynamics).

Bear in mind, however, that the likelihood is 1000 to 1000000 times
greater that any erroneous results obtained on a Pentium are due to
software errors, rather than any error in the CPU.  For the average
user, I do not believe the bug has a significant impact,
particularly in comparison to other sources of error.

However, for users in mathematics, science, and engineering, we
must each be our own judge as to the danger posed by the bug.  In
any case, whether you are using the Pentium or some other CPU,
mission-critical applications and those which may affect the health
and welfare of others should be performed in duplicate, preferably
on systems with different CPUs, operating systems, and application
software.


/***************************************************************/
Q4:  Why did Intel contact you for a collaboration? Don't you think
that people might interpret it as a way of buying your silence? 
Some observers find this quickly signed NDA surprising.
/****************************************************************/


RESPONSE:  Intel has indicated that they are interested in having
me as a consultant because I am clearly doing a type of
mathematical work that they did not previously anticipate the
Pentium being used for; consequently they did not conduct their
stress and validation tests on the Pentium with this type of
application in mind.  Apparently they would consider it a useful
additional test of their future steppings and chips to see if these
processors can correctly perform calculations of these types to the
standards of accuracy which I require.

The NDA was signed as part of an application process normally
required of individuals or companies which act as independent
contractors for Intel.  As I have pointed out before, I accept full
responsibility for misinterpreting the intent and force of the NDA.

After the NDA became an issue, Intel went out of their way to make
clear to me that it did not apply to information concerning the
discovery that I had made; it was only relevant to confidential
information the parties might exchange in any future consulting
work (for example, proprietary information about a CPU before it
had been released to the public).  As I have explained before, my
misinterpretation was primarily a consequence of the fact that I
once held a Q-clearance for critical nuclear weapon design
information at Los Alamos National Laboratory, and the
interpretation enforced there is much, much stricter; even
information acquired in the open, prior to signing the clearance,
is considered "born secret" and subject to nondisclosure.

Why, you might ask, would I sign the NDA if it might have the
effect (due to my own mistaken interpretation) of silencing me
regarding the bug?  Perhaps I did not give it enough thought.  On
the other hand, I had to consider the value to myself, and to my
employer (Lynchburg College), of a possible long-term relationship
with a corporation which could provide benefits and prestige for
both of us.  I had already made the bug public; my original
announcement and code were available almost worldwide at this
point, so I certainly felt I had done my duty to the general
public.  Clearly Intel knew that no agreement with me could put the
genie back in the bottle.  I was trying to look at the possibility
of an association with Intel in terms of its long-range impact. 
These are the kinds of decisions that are always easy to criticize
if you do not have to make them yourself, without advice, under
pressure.

At this point (9 December), Intel and I have agreed to suspend all
negotiations until the furor over the bug settles down.  I am not
an employee of or consultant for Intel; Intel has paid me no fees,
either in the form of cash or equipment (they have provided me with
bug-free replacement chips for the two Pentium systems I have been
using).  The NDA has no effect at this time, since we have in fact
not exchanged any proprietary or confidential information.  Perhaps
after the first of the year, if my health allows, we will again
explore the possibility of a relationship (on 19 December, I must
enter the hospital for a heart procedure, possibly a coronary
bypass; this will be the third such procedure in 13 months).


/***************************************************************/
Q5:  What does this FDIV problem signify at the logical level of
the FPU?  Does it occur with some specific mantissa schemes?
/***************************************************************/


RESPONSE:  The difficulty apparently arises from an error in the
lookup tables used to implement the hardware division algorithm;
the lookup tables are either incorrect or incomplete.  The Pentium
apparently attempts to use a much more aggressive algorithm for
hardware floating point division than did the 486; this is
indicated by the fact that it uses only about half as many clock
cycles per floating point division.  Evidently the 486 is
attempting to generate one bit of the quotient per iteration, while
the Pentium attempts to generate two bits per iteration.  In every
case of which I am aware that produces an error, the first 16 bits
of the mantissa (in an 80-bit temporary real) are 0xBFFF.  Only a
small portion of even these mantissas produces an error, however
(roughly 1 in 1e5, or less than one in 1e9 of all possible
mantissas).  The exponent appears to be irrelevant.  The worst case
error posted to date is the one discovered by Tim Coe, an engineer
at Vitesse Semiconductors:  4195835.0/3145727.0 is returned
correctly to only 14 significant bits (the 5th decimal digit and
all beyond are in error):

4195835.0/3145727.0 = 1.333 820 449 136 241 00  (Correct value)
4195835.0/3145727.0 = 1.333 739 068 902 037 59  (Flawed Pentium)

Brooke Crothers reports in "Infoworld" (5 December 1994, page 1)
that Intel has confirmed the existence of cases where the fourth
decimal digit is also in error, but I know of no specific example
where the result does not at least round correctly to the fourth
significant decimal digit.

Note that the FPU instructions FPREM and FPREM1 (floating point
remainders) are also subject to the bug.  In fact, it was probably
one of these that caused my original 13 June error, rather than the
FDIV instruction.


/****************************************************************/
Q6:  Do your calculations of the relative frequency of the error
agree with those publicized by Intel?
/****************************************************************/


RESPONSE:  Yes, for all practical purposes.  Intel quotes an error
rate of about 1 in 9.5e9 random divisions.  I obtain a rate of 1 in
31e9 for random divisions and 1 in 1.26e9 for random reciprocals.
The rates may not be directly comparable, since Intel is apparently
including single and double precision operations in their count,
and I am testing only long double divisions and reciprocals (since
this is the natural data type for the FPU stack, and since it is
the relevant data type in my own research).

Note, however, that many authorities consider statistical sampling
rates to be unrepresentative of the problem, since the values
appearing in a particular application may not constitute a random
sample of all possible mantissas.


/****************************************************************/
Q7:  Do the replacement Pentium chips you received from Intel
appear to eliminate the bug?
/****************************************************************/


RESPONSE:  Yes.  I have tested the replacement chips with > 1e15
simulated divisions and reciprocals and have observed zero errors. 
The critical cases, such as my original example and Tim Coe's
example, have also been tested individually.


/***************************************************************/
Q8:  What about the so-called "workarounds" for the bug?
/***************************************************************/


RESPONSE:  The workaround suggested by Cleve Moler of MathWorks
consists of replacing each division by a function call.  The
function call first performs the division directly, then tests the
answer for correctness (e. g., by comparing x*(y/x) to y).  If the
result is in error due to the Pentium bug, the numerator and
denominator are each multiplied by 3/4 (which destroys the 0xBFFF
denominator mask causing the problem) and the division is repeated. 
This process is continued in a loop until the result checks
correctly.

I use a similar workaround in my sample code, but use a multiplier
of 3 rather than 3/4, which would appear to be two clocks faster.

Of course, the workaround only works for applications whose code
has been rewritten, recompiled, and reshipped since the bug
appeared. Previously existing binaries can avoid the bug only by
locking out the FPU (e. g., by setting 87=NO and NO87=NO87 in DOS,
or by resetting the emulation bit in the machine status word of CR0
otherwise).

The workaround slows the machine down slightly, perhaps 30 % (this
is application dependent).  Locking out the FPU may slow the
machine down by a factor of five or ten, depending on the
application.

A separate workaround is required if the floating-point remainder
instructions, such as fmod or fmodl in C, are used.


/***************************************************************/
Q9:  Why do you think this particular bug has received an
inordinate amount of publicity, making it such a public relations
nightmare for Intel? 
/***************************************************************/


I believe several factors contributed to this phenomenon.

*    Intel's initial failure to publicize the problem, even in a
     listing of errata to their OEMs and most valued customers, was
     in retrospect a mistake which alienated these constituencies.

*    Intel's subsequent response, once the bug had been detected  
        independently, was considered unsatisfactory by nearly
     everyone outside the company.

*    The Pentium CPU has been the subject of a high-profile
     advertising campaign by Intel.

*    In contrast to most previous errors found in CPUs, this one
     occurs in an elementary, frequently-used operation which is
     easy to demonstrate to the non-specialist, even those who have
     little or no computer training.

*    The bug was found late in the life cycle of the chip, after
     millions of them were already distributed or in production.

*    The existence of the Internet, and its current widespread
     availability, caused the news and the reaction to Intel's
     response to spread much more rapidly than for previous bugs.


/***************************************************************/
Q10:  Can you tell us something of your own background?
/***************************************************************/


I was born 6 February 1943, in Wareham, Massachusetts, but grew up
in the coal mining town of Amherstdale, Logan County, West
Virginia.  My father and most of my male relatives were coal
miners; my father died in 1973 due to heart disease caused by black
lung disease.  I graduated from Man High School in Logan County in
1959; earned a B. S. degree in physics from West Virginia
University, Morgantown, West Virginia, in 1963; an M. S. degree in
theoretical physics from WVU in 1965; and earned the Ph. D. in
applied mathematics from the School of Engineering, University of
Virginia, Charlottesville, Virginia, in August, 1971.

I have spent nearly all of my professional career as a professor of
mathematics at Lynchburg College, Lynchburg, Virginia, beginning in
1968.  Lynchburg College is a small (full time undergraduate
enrollment about 1420), private, non-profit, coeducational liberal
arts college, most generally noted for its excellent programs in
the fine arts (dramatic arts, art, music) and its success in
Division III (non-scholarship) athletics.  The College was founded
in 1903 by Dr. Josephus Hopwood, and is an ecumenical, non-
sectarian institution affiliated with the Christian Church
(Disciples of Christ).

I did take a leave of absence in 1985-86 to work as a staff member
in X Division (nuclear weapon and nuclear reactor design and
analysis) at Los Alamos National Laboratory, Los Alamos, New
Mexico, but decided I preferred the academic environment.  I also
do consulting work for the Avalon Hill Game Company, Baltimore,
Maryland, producing the team charts and rules each year for the
"Paydirt" tabletop football game originally developed by Sports
Illustrated Enterprises, and also the team charts and rules for
"Bowlbound," the college football edition of the game.

My wife of 21 years is a practicing HVAC mechanical engineer and
consultant, Linda Carol Taylor Nicely, a graduate of the School of
Engineering at the University of Tennessee.  We have no children,
but have the good fortune to enjoy the company of six cats.


Sincerely,





Dr. Thomas R. Nicely

IBM Halts Shipments of Pentium-Based Personal Computers Based on 
Company Research

December 12, 1994

SOMERS, N.Y., Dec. 12, 1994 . . . IBM today announced it has
stopped shipment of all IBM personal computers based on the Intel
Pentium* microprocessor.   The action is based on tests conducted
by the IBM Research Division stimulated by growing customer
concern that Pentium-related problems are more frequent than
previously estimated.

Results of IBM Research Division tests indicate that while
Intel's descriptions of the flaw are technically accurate, there
are many customer situations in which the risk of error may be
significantly higher.

IBM is working with customers on interim solutions and will
resume shipments upon customer and business partner request.
Also, IBM is:

     -- Sharing its analyses with customers and the industry on
the Internet: http://www.ibm.com/Features/pentium.html

     -- Working with IBM customers to help guide them in their
own specific risk assessments.

     -- Providing for replacement of flawed Pentium chips at no
cost to customers.  This applies to all its Pentium-based PCs,
either those already installed or systems that will be shipped
prior to new chips being available.

     -- Working with Intel to help resolve Pentium-related
problems as quickly as possible.

"We believe no one should have to wonder about the integrity
of data calculated on IBM PCs," said G. Richard Thoman, IBM
senior vice president and group executive.  "Many of our
customers have indicated concern since the Pentium flaw was
disclosed.  We've conducted our own tests and concluded that the
risk of error is significantly higher than previously thought and
warrants today's actions."

Intel has said that in purely random situations the
likelihood of a customer encountering an error is only once in
27,000 years and that off-the-shelf software is not affected.
However, IBM tests indicate that common spreadsheet programs,
recalculating for 15 minutes a day, could produce Pentium-related
errors as often as once every 24 days.  For a customer with 500
Pentium-based PCs, this could result in as many as 20 mistakes a
day.

Pentium-based systems currently shipped by IBM are the
ValuePoint P60, the IBM PC 300 P60 and 700 P90, the Aptiva 710
and 730 models and IBM PC server models 85, 95, 300 and 500.

Please Note:
Questions about the content or currency of this press release
should be directed to your local IBM representative.
 

Intel Says IBM Shipment Halt Is Unwarranted

SANTA CLARA, CA, December 12, 1994 -- In response to an IBM press release,
Intel reiterated that it has studied the Pentium(tm) processor flaw for
months and has concluded that the frequency of encountering reduced precision
in floating point divide operations is once in every nine billion random divide
operations. Intel said it regards IBM's decision to halt shipments of its
Pentium processor-based systems as unwarranted. 

"Based upon the work of our scientists analyzing real world applications, and
the experience of millions of users of Pentium processor-based systems, we have
no evidence of increased probability of encountering the flaw," said Andrew S.
Grove, president and chief executive officer. 

"You can always contrive situations that force this error. In other words, if
you know where a meteor will land, you can go there and get hit," Grove said. 

Intel does not agree with the conclusions reached by IBM, but reiterates
nonetheless that any customer who might encounter the problem with the Pentium
processor in the course of their applications will be sent a replacement at any
time during the life of their PC. 

Intel, the world's largest chip maker, is also a leading manufacturer of
personal computer networking and communications products. 

CONTACTS:       Howard High
                Press Relations
                (408) 765-1488

                John Thompson
                Press Relations
                (408) 765-1279

                Gordon Casey
                Investor Relations
                (408) 765-8418

    This morning on WBUR, a spokesman from Lotus said "with a few simple
    commands, 1-2-3 can work around the Pentium bug"
    
    I don't know if they were talking about a general FPU disable, or
    something 1-2-3 specific.
    
    Me, I'm lucky enough to only have a 486..
    
    ...tom

Re: WBUR

I heard the blurb on WBUR - they did indeed say that "Digital insists the
bug would be seen once in 27000 years" and didn't say that that was actually
Intel's position.

				Steve

I haven't seen it said in so many words, and maybe some of the PCBU is
listening (I believe they have to define our posture), so I
ask/suggest/propose that Digital adopts and advertises the following
position:

"Upon request, Digital will replace defective Intel Pentium CPUs in
Digital PCs with Intel's replacement chip when it becomes available.
This will be done at no cost to the owner of the Digital PC.

"Digital Equipment Corporation is taking this position because we
believe our customers deserve the best products, fair treatment, and
the support of the only PC vendor who will do 'whatever it takes' to
sustain and reinforce our long history of customer satisfaction."

Beyond that, we fight our own battles with Intel to be compensated for
the material and labor involved in the switch.

JMHO,

Pete

    Second the motion!
    

    Now, get it out to the news.  This morning's paper mentioned "major
    computer manufacturers" using Intel's chip and how they would handle
    it.
    
    IBM quit shipping Pentium-based systems.
    
    Packard Bell and Gateway say they've had no customer complaints, so
    business as usual.
    
    Digital isn't mentioned.

Hey, I've just figured out the solution.  All I have
to do is to deliberately execute a single FDIV with 'bad' operands,
and then I'll get 27000 years of trouble-free division.
Right?

Saw another blurb saying that Compaq is doing the same as Digital. I think
we'd be in much worse shape if we did not take the same position as the
vast majority of suppliers of pentium systems. Will it hurt Compaq?

Its not what we say, but how we say it.

>Per

re: .136

And here's an internal IBM memo that's been widely forwarded on the
Internet.  In it, IBM responds to Intel's criticisms of it's decision to 
suspend Pentium shipments.

-----------------------------------------------------------------
 To: US PC COMPANY EMPLOYEES

 FROM:    G. Richard Thoman
          Senior Vice President and Group Executive
 SUBJECT: Pentium


 Dear Colleague,

 The purpose of this note is to describe the basis of IBM's recent
 decision to temporarily stop shipment on our Pentium-based PCs.
 After receiving the results of our own tests concerning the flaw with
 the floating point unit in all Pentium processors, IBM made the
 decision to fully disclose our findings to our customers, competitors,
 Intel and the industry.

 The decision to temporarily stop ship while we disclosed our findings
 was made to give all customers a chance to evaluate the data and decide
 whether they want shipment.  We also agreed to replace flawed chips
 in previously installed and yet-to-be installed systems without
 question at no cost to the customer.

 The following information is the basis for our decision. Although IBM
 and Intel may disagree on assumptions, we are still working together
 to best resolve the problem.  Fortunately, Intel has a fix and will
 begin shipping corrected processors over the next few months.

 If our customers need further information, including Pentium processor
 replacement, please call or have them call 1-800-426-3389.
 To keep call volumes down, please restrict the use of this number for
 customer related issues.

 We view this as a short-term problem and are working to get replacement
 chips to customers as quickly as Intel can provide them.  Details on the
 schedule dates for replacement of chips will follow pending
 further information from Intel on the availability of corrected Pentium
 chips. The options available to dealers, retailers and customers who
 are expecting shipment of, or have installed Pentium-based PCs from IBM,
 are outlined at the end of this note.

 Decision Basis:

 On November 22, Intel acknowledged a defect with the floating point
 unit in all Pentium processors. Intel characterized the flaw as
 affecting one in nine billion calculations, estimating errors
 once in 27,000 years with no affect on off-the-shelf applications.

 Based on their statements, IBM initially issued a statement that said
 we would replace flawed Pentium chips upon customer need.

 However, in response to customer concern over data integrity and growing
 activity on the Internet of independent scientists and mathematicians
 who were questioning Intel's conclusions, we conducted our own tests to
 validate Intel's findings as outlined in an Intel white paper.

 No one disputes the fact that there is an error with the floating point
 instruction unit in the Pentium.  Our disagreement is on the
 characterization of risk.  According to an Intel white paper, Intel
 reached their conclusions by making two key assumptions when conducting
 their tests:

      - Intel assumes that any one number is as likely to occur as
        another.  In other words, Intel is claiming that a number such
        as 659.8943872 is as likely to occur as say the number 6.

      - Intel also claims that average spreadsheet users do about
        1,000 floating point divisions per day.

 In analyzing the Pentium problem, IBM made two different
 assumptions in an effort to simulate a more realistic customer computing
 environment.  We wanted to answer for our customers how likely would
 there be a risk to data in plausible customer environments.

      - Our information regarding how customers use data, shows
        that customers are more likely to use certain numbers over
        others.  Therefore, our tests focused on calculations
        using often-used 3- and 4-digit numbers such as $4.57 or
        $12.32.

      - When we added or subtracted ten random numbers having
        three digits, one out of every 300 of the results were
        likely to produce an "at risk" number -- that is, a number
        when used as a denominator in division will produce an
        error.  If we repeated the test with numbers having four
        digits, then one out of every 2,000 numbers could cause an
        at risk number.  This is significantly higher than Intel's
        assertions.

      - The second point we disagreed with Intel is on the average
        number of divisions an average spreadsheet user does.
        According to PC Magazine UK, which researched the
        habits of spreadsheet users, typical users of an
        off-the-shelf spreadsheet conducts about 5,000 divides
        every second when they recalculate a spreadsheet.

      - Based on this PC Magazine data, if a user does only
        15 minutes of recalculations a day, he will
        perform 4.2 million divides a day.

      - Using this data along with the numbers customers are
        likely to use in an actual spreadsheet, our tests
        concluded that a user is likely to make a mistake every 24
        days.

      - If a customer has 500 Pentium systems installed this could
        result in 20 mistakes a day.

 Our study is an analysis based on probabilities.  In reality, a user
 could face either significantly more errors or no errors at all.  If
 an error occurs, it will first appear in the fifth or higher significant
 digit.

 After receiving the results of the tests, which were given to two
 independent parties who reviewed and agreed with our findings, we
 made the following decisions:

 1) Fully disclose our findings to our customers, competitors,
    Intel and the industry so they can evaluate our research.

 2) Temporarily stop ship on the Pentium-based PCs until customers
    have a chance to evaluate the data and decide whether they
    want shipment.

 3) Reassure all customers that we will replace the flawed Pentium
    processors in systems that have already shipped or those yet to be
    shipped, at no cost to customers.

 Dealer/Retailer/Customer Directions:

 The options available to dealers, retailers and customers who are
 expecting shipment of Pentium-based PCs from IBM are:

      - If customers need high-performance PCs immediately, they
        need to consider if they can substitute a 486 class
        systems such as a DX4.

      - Dealers, retailers and customers need to evaluate if they can
        defer the shipments until the first quarter until new
        chips are available.

      - If dealers, retailers or customers determine they need a
        Pentium-class system and they want to accept shipment, we
        will ship products and replace the defective chips as
        soon as possible.

      - This is not a recall.  IBM will replace defective
        Pentium chips in systems already installed at no cost to
        the user.

 Replacement procedure:

      - Details on the schedule dates for replacement of chips to
        follow next week pending further information from Intel on
        the availability of corrected Pentium chips.

 Regards,
 Rick
-----------------------------------------------------------------

    >    Second the motion!
    
    Third it, etc.
    
    >    Now, get it out to the news.  This morning's paper mentioned "major
    >    computer manufacturers" using Intel's chip and how they would
    >	handle it.
    >		. . .
    >    Digital isn't mentioned.
    
    Well, you said *major*.  :-)  Another note shows we're not in the top
    10 in US PC sales -- and to the general US press, there is nothing else.
    
    >	Hey, I've just figured out the solution.  All I have
    >	to do is to deliberately execute a single FDIV with 'bad' operands,
    >	and then I'll get 27000 years of trouble-free division.
    >	Right?
    
    Right -- if you only do one FDIV a year.  Hope you didn't buy a Pentium
    just for that!  :-)
    
    -Mark

Intel will likely not call the P6 (the successor to the Pentium) Hexium!

    Has anyone detected any movement in Digital's (PCBU's) position
    yet? The combined Intel/Digital messaging refers to the 1 in 27000
    year theory which is pretty much moving to an industry laughing
    stock status.
    
    I personally don't care whether we do the right thing or whatever it
    takes but our current positioning doesn't seem to reflect either.
    
    There are those who would brand IBMs actions as a marketing ploy.
    Well, that may be true. But it may also be true that IBM is showing
    a more genuine concern for resolving its customers worries than we
    are right now.
    
    There's an old saying that action speaks louder than words. Well, the same
    thing applies to inaction too.
    
    I'm reminded of a (true) anecdote about a board of directors of a
    company who had just been presented information about faulty equipment
    being at certain customers. It would (of course) be very expensive to
    replace so a debate ensued on the relative risks and costs of being
    sued, loss of image, chance of discovery etc. After a while the
    president (and owner) of the company walked in and the board started
    presenting the pro's and con's to him. After about 30 seconds the
    president sat bolt upright: "You mean we have faulty equipment out
    there and you know about it??? Replace it immediately." End of 
    analysis. End of debate. End of story.
    
    re roelof

    During the great burning of Rome, even Nero realised that he couldn't
    fiddle and sit on his hands at the same time.
    
    So what if IBM's stance is 100% marketing, WHY DON'T WE DO SOMETHING,
    ANYTHING, TOO! We should be making use of a golden opportunity to a)
    show we are a real player in the PC world, and b) show off Alpha.
    
    I get so frustrated at this company sometimes. Don't these people read
    Internet? (Silly question, after all, there's no business need, waste
    of resources blah, blah).
    
    Cheers, Laurie.

Compaq announced yesterday that it would continue to sell Pentium systems
and would not automatically replace chips.

					Steve

 From the Public Relations Department...

                  DIGITAL CONTINUES SHIPPING PENTIUM SYSTEM
                      
 Mass. -- December 13, 1994 -- Digital Equipment Corporation stated
 today that Digital will remain a reliable supplier of Pentium products.
 The company's Personal Computer Business Unit is continuing to market and
 ship Pentium-based PCs.
     "Although we are receiving some requests for information about the
 current Pentium situation, customers continue to choose Pentium systems,"
 said Howard Elias, Vice President of Desktop Systems for Digital's Personal
 Computer Business Unit.  "We intend to fully honor their choice by
 supplying Pentium PCs.
     "Customer satisfaction is at the heart of how Digital is handling the
 Pentium situation.  Digital has put in place an internal support team to
 ensure that our customers receive a fast and effective response to their
 needs.  We continue to work closely with Intel on a daily basis to make
 sure any customer with an affected application who needs a chip gets one as
 soon as possible.  And, we are mobilizing Digital's worldwide Multivendor
 Customer Service organization to help customers work with Intel to assess
 the issue in terms of their applications, and to install new chips when
 needed," Elias continued.
     Digital Equipment Corporation is the world's leader in open
 client/server solutions from personal computing to integrated worldwide
 information systems.  Digital's scalable Alpha platforms, storage,
 networking, software and services, together with industry-
 focused solutions from business partners, help organizations compete and
 win in today's global marketplace.
                                    ####

Note to Editors:  Digital and the Digital logo are trademarks of
                  Digital Equipment Corporation.  Intel and Pentium
                  are trademarks of Intel Corporation.

CORP/95/757

> Intel will likely not call the P6 (the successor to the Pentium) Hexium!

Well, how about Sexium?

___Pete

    Is this problem with the Pentium one of the first signs of Intel
    hitting a CISC wall with the X86 architecture?  Is it going to be
    harder and harder for them to design and verify chips with the
    increases in complexity needed for performance improvements?

    Is it less likely for a RISC architecture to have a problem like the
    Pentuim's because of the fewer number of instructions implemented in
    silicon?  Does this make it easier to design and test?  With the Alpha
    architecture could similar bugs be corrected with changes to the PALcode
    or compilers?

    Just curious.

    thanks,
    Fran

    Well ....
    
    For all of those expressing outrage and indignation that we are not
    "doing what it takes": Are you willing to give up your job to finance
    the replacement of all the Math-challenged Pentuim chips DEC has sold?
    
    It would be irresponsible for us to make shoot-from-the-hip statements
    about mass replacements before a process is developed to implement it
    and have Intel foot the bill. If it was a DEC chip, and a fix was now
    available, we would use the FCO (Field Change Order) process to handle
    it, and the engineering group responsible would pay for it. This ain't
    a DEC chip folks ... if we just go buy a train load some DEC employees
    will pay for it with their jobs.

   What's the replacement cost going to be?  $100?  At $100,000 per
   employee per year burdened rate, that's 1,000 replacements per job.
   
   We have already sacrificed tens of thousands of employees in making the
   transformation from low-volume, high-profit vendor to high-volume,
   low-profit vendor.  At this point, frankly, what's a few more?

    I would guess that our replacement costs would exceed $100 per even if
    Intel gave us the chips for free.
    
    I think that computer companies ought to recall products like car
    companies.  Safety defects are totally replaced, performance defects
    are replaced when the customer complains, and some problems (which are
    never classed as a defect) are settled at the service manager's
    discretion.
    
    Mark

    I don't know how he can dance around the issue like this.
    
    
    There is an aknowledged defect.
    
    DIGITAL is obligated by the terms of it warranty agreement to FIX IT.
    
    Digital can do that any way it sees fit but it is still responsible
    to fix it.
    
    
    Brian V
    
    Getting very disgusted
    

    re: .152
    > Is this problem with the Pentium one of the first signs of Intel
    > hitting a CISC wall with the X86 architecture?  Is it going to be
    > harder and harder for them to design and verify chips with the
    > increases in complexity needed for performance improvements?

    I don't believe there's really a CISC vs RISC issue here -- at a chip
    level, RISC chips are just about as complex as CISC chips, and require
    just as rigorous a testing cycle.  
    
    > Is it less likely for a RISC architecture to have a problem like the
    > Pentuim's because of the fewer number of instructions implemented in
    > silicon?  Does this make it easier to design and test?  With the Alpha
    > architecture could similar bugs be corrected with changes to the PALcode
    > or compilers?
    
    In some ways, I think a RISC chip could be more difficult to test,
    as it may be more difficult to exhaust all the possible instruction
    streams.  Deep piplines and multiple issue makes testing particularly
    complex.  It may be easier to provide a fix in a compiler for a RISC
    chip, since more of the "intelligence" is moved up from the hardware
    level to the compiler level.  But overall, I think it's really a wash. 
    Intel just had a hole in their testing methodology.  It's
    impossible to verify every possible code path and processor state, so
    you end up making a tradeoff between the level of confidence in your
    verification vs. time-to-market.
    
    One good thing that I hope comes out of this is a reality check on the
    importance of exhaustive hardware verification.
    
    	Steve

      I just purchased a DIGITAL PENTIUM-90 system.  As a customer,
      I would like Digital to send me notification of the problem
      (i.e., not to assume that I've been listening to all the 
      controversy!  I would like them to tell me how to schedule
      their replacement of
      the defective chip that they put into my system, with a
      corrected version.
            I am willing to listen to suggestions about priorities, with
      regard to the applications that I use today, but I believe that -
      as the customer - I have the final say over how I am impacted and -
      as the vendor(s) - DIGITAL/INTEL needs to take my needs into account
      and do what I think is the right thing!
            Also, as an employee of DIGITAL, I want us to be squeaky-clean
      and be seen as "highly ethical" in dealing with this unfortunate
      incident.  We did not make the problem, but we must do our part
      to help fix it.  I really feel we have a good business opportunity
      here - better than all the fancy advertising bought with big $$$$!
    
            just my opinion
    
                    Dick
                                                                   
     

    re: .148     -< Whatever it takes? HAHAHAHA! >-
    
    I was amazed to hear a sound bite from a high-ranking IBM rep,
    commenting on their position in this matter:
    
    "We'll do whatever it takes to [fix the customer's problem, etc.]"
              *****************
    
    Augh!  Painful it was...
    
    Chris

    Yeah ... well, after the trashing IBM has given Intel and Andy in
    the press the past week, they may have to stand in line behind us
    to get replacement chips. At least I hope so ....
    

    Intel has released a 30 page white paper giving its insights into
    the FDIV error. It is available in both postscript and PDF format
    and you can pick up a copy at http://www.intel.com.
    
    I am pleased with the press release in .150 the gist of which is
    "customer we will help solve your problem if you have one". This is
    a far cry from the initial messaging which said more or less "nothing
    to worry about and if you are go call Intel". This is, simply put,
    doing the right thing.
    
    The Dutch Consumer Bond has issued a statement that the position
    taken by Escom (Europes first or second largest PC distributor) 
    wrt the Pentium chip (basically: want a chip replacement? Call
    Intel) is against Dutch consumer law.
    
    And as one bright wag on the Internet remarked: "Just when we're
    getting a handle on this CISC vs RISC thing along comes CISC vs
    RISK..."
    
    re roelof        
    

    re: .153
    
    If you buy (say) a SHARP television and the tuner fails a month
    after purchase while under warrantee, how would you like SHARP to say
    "That's a Mitsumi tuner.  They know it's bad.  Call them for a
    replacement.  And, no, we won't install it for you."?
    
    Fixing a commodity item is part of doing business.  If we're not
    prepared to fix non-functional goods under warrantee, we should not be
    in this business.
    
    If the Intel component costs us money, we should be pursuing that with
    Intel, not hanging customers out to dry.
    
    -- Russ

    It seems my point in .153 is being missed. This is not a new situation
    for Digital. We have had a process in place for many years to handle
    it. I have done scores ... probably hundreds ... of FCOs to DEC
    products over the last 16 years. The process of developing and
    delivering an FCO is in place. And right at this moment, we couldn't
    replace everyone's Pentuim for any reason. We don't have any to do it
    with! Now if the only thing that's going to make you feel warm and
    fuzzy is to have some PR-drone spout slogans then I guess you'll just
    have to be dissapointed. I think the wording of .150 is appropriate.
    
    I wish the Pentium based PCs were the only things we've ever sold that
    didn't perform as intended. They are just the one's that got on the
    nightly news. We've had a few products over the years that we FCOed to
    death, and they never worked right. But, since Ozzie and Harriet didn't
    have one in the den the news media didn't care. 
    
    The comparison between the Pentium situation, and a TV with a broken
    tuner is way off base for several reasons. First, the Pentium chip
    didn't "fail". It has a subtle design flaw. Second, with most consumer
    electronics the majority of components can be second sourced. If chip
    maker A's flip-flops don't flop right, you go buy some from chip maker
    B. You can't buy Pentiums from anyone but Intel. Third, nobody has
    said we won't install the replacement. I'm sure that once the things
    happen that need to happen I'll be replacing a number of them, I'll
    be happy to replace yours, as soon as an FCO is available and I have
    an EQ part number I can order. If that isn't happening fast enough
    for you, then why don't you send the PCBU or Intel a resume and explain
    how you can help them speed it up.
    
    We spent millions over the years FCOing everything from TS11s to
    RA82s to VAX9000s. I'm sure we'll spend some more to FCO our Pentium
    PCs too.

    ...can be found at
    
    http://Boole.Stanford.EDU:80/pub/FDIV/
    
    It consists of his 30 (!) postings on the subject. For theory
    freaks only.
    
    re roelof

    ...can be found at
    
    http://www.mathworks.com/NYT_Dec14.gif

This rebuttal including bar chart graphics can be found at:

http://www.intel.com/product/pentium/ibm/ibmss.htm

INTEL'S REVIEW OF IBM'S CLAIMS 

I. Overview

Intel has continued its review of IBM's claims that contradict Intel's 
detailed analysis of the Pentium(tm) processor floating point flaw. 
Actual data from real world applications confirms Intel's estimates, 
and contradicts IBM's claims.

IBM questions Intel's estimates in two ways: (i) IBM asserts that 
certain bit patterns susceptible to the Pentium processor's floating 
point divide flaw occur with increased frequency in the course of 
calculations such as those typically performed in a spreadsheet 
application with financial data; and (ii) IBM also asserts
that typical spreadsheet users perform divide calculations at a 
dramatically higher rate than estimated by Intel.

For this review we studied data drawn from real spreadsheet 
applications in representative user environments (this is in addition 
to the exhaustive analysis described in the Intel white paper). Data 
has been collected from hundreds of spreadsheets throughout Intel. 
Our sample applications were collected from the various
functions within Intel, including Finance, Sales & Marketing, 
Planning, Treasury, Product Engineering, Production Control and 
Tax/Customs.

II. Frequency of Suspect Bit Patterns in Denominator

Bit patterns susceptible to the floating point divide flaw all 
contain a string of more than six 1's in their binary representation 
(although not all numbers with this pattern are at risk). To test the 
IBM assertion that denominators with suspect bit patterns occur more 
frequently than random, we measured the bit patterns fed as 
denominators to all the floating point divides encountered in fully 
recalculating our sample of spreadsheets. Our findings are presented 
in Figure 1.

Figure 1
[Figure 1 is a bar chart with two columns: one showing random
frequency, the other showing measured frequency. The chart shows
that measured frequency as about a factor 4 _smaller_ than
random frequency. roelof]

As this figure shows, the measured frequency of the bit patterns that 
are necessary (but not sufficient) for an at risk denominator is 
0.48%, actually below the expected random frequency of 1.5625%. Put 
another way, while IBM asserts that the frequency of encountering 
floating point divide errors based on denominators with
several consecutive 1's in spreadsheets is 1 in 100 million vs. 
Intel's claim of 1 in 9 billion, the measured frequency is in 
fact even less than 1 in 9 billion. 

In their analysis IBM focused on expressions such as (a.b) - (c.d), 
an example of which is 4.1-1.1, which is calculated to be 
2.9999999999999. This number has a long string of 1's in its binary 
representation. However, not only does the actual data show that these 
numbers are no more likely to occur than other numbers as a
denominator, but in fact when such a number does trigger a reduced 
precision result, the inaccuracy shows up at worst in the 12th 
significant decimal digit. IBM neglected to mention this fact.

III. Frequency of Floating Point Divide Operations

A second IBM assertion is that a spreadsheet recalculation running 
on a Pentium processor-based PC can perform about 5000 floating point 
divide operations per second. Based on this, IBM assumes that a 
typical user will execute recalc's for 15 minutes/day, thus performing 
4.2 million floating point divide operations daily. IBM presents no 
data to support this assumption. Intel has concluded that a basic 
spreadsheet user will perform approximately 1000 floating point divides per day.

As the measurements in Figure 2 indicate, nearly 70% of the 
spreadsheets in our survey involved fewer than 1000 floating point 
divide operations, and virtually all of the spreadsheets (other than 
the most intensive financial and engineering applications) involved 
fewer than 10,000 divides.

[Bar chart with 6 columns showing Gaussian-like distribution of 
number of divides in the spreadsheet sampling. Peak (approx. 35%) at 
101-1000 divides. roelof]

Figure 2

Based on these measurements and our ongoing survey of how users 
interact with these applications in terms of the number of 
spreadsheets opened per day by a typical user (approximately 1-3), 
the number of recalc's performed per spreadsheet (approximately 1-3), 
and the percentage of overall formulae involved in a recalc
(about 25%), we remain confident of our conclusion that the basic 
spreadsheet user performs fewer than 1000 floating point divides in 
a day.

IV. Conclusion

IBM made two assertions counter to Intel's white paper that led to 
IBM's conclusion that a computer based on the Pentium processor could 
return a reduced precision result every 24 days. The data presented 
here, which supplements the data provided in the Intel white paper, 
proves that IBM's assertions are incorrect, and strongly supports 
Intel's analysis of the impact of the Pentium processor's floating 
point divide flaw. This flaw is of no significance in the commercial 
PC market as the average spreadsheet user is likely to encounter a
failure only once every 27,000 years.


*This is a summary of a paper entitled "Intel Analysis Refutes IBM's 
Claims" by M.L.Barton, Ph.D., Staff Computational Scientist, and 
R.A.Passov, Senior Treasury Manager, Intel Corportaion. Intel 
Corporation December 16, 1994 

    re: .163
    
    Your point regarding the single-source nature of the Pentium and lack
    of current fix is not in dispute.
    
    What I _DO_ dispute is that we shouldn't "fall on our swords" for
    Intel's error.  It doesn't matter if it is Intel's part or not.  It's
    our box.  It's our problem.  When the fix is available, we should
    provide it.  It shouldn't wait until we get Intel to fund it -- it's
    our customer, it's our problem.  If we think Intel should foot the
    bill, we should pursue that independent of servicing OUR customers.
    
    No one forced us to get into the commodity business.  We chose to.  If
    we can't play by the rules of a commodity business, we are fooling
    ourselves if we think we'll survive or become a top player.
    
    We keep telling customers that we're the best PC provider with the best
    products and services.  We have a chance to prove it.  When Intel fixes
    the problem, we should fix the PCs without hassles to our customers. 
    Then we can say "What's the Digital difference in PCs?  We stand by our
    products.  Can you say that about your xxxxx PCs which still have those
    buggy Pentiums?"
    
    If we want to be the cream, we have to be willing to rise to the top.  Few
    people will pay cream prices for something that looks and tastes like 
    skim milk.
    
    -- Russ

    In his message (.83) Andy Grove says:
    
   �The Pentium processor was introduced into the market in May of '93
   �after the most extensive testing program we at Intel have ever
   �embarked on. Because this chip is three times as complex as the 486,
   �and because it includes a number of improved floating point
   �algorithms, we geared up to do an array of tests, validation, and
   �verification that far exceeded anything we had ever done. So did many
   �of our OEM customers. We held the introduction of the chip several
   �months in order to give them more time to check out the chip and their
   �systems. We worked extensively with many software companies to this
   �end as well.
    
    According to a German computer rag (I think it was c't) the fault is
    detected by a FPU test program that has been distributed for free for
    ~3 years by - you guessed it - Intel!
    

    I think they are refering to a program that Intel has written and
    distributed to check out compatibility of 387-type floating point 
    Co-Processors. Not surprisingly, some of the clone makers failed that
    test. 
    
    Note that this test program does test only for 387-compatibility. 
    It seems that this program also fails on the Pentium FPU, 
    telling us that a Pentium is as much compatible to a
    387 as an of the 387-clones on the market :-)
    
    It doesn't check for the FDIV bug however.
    
    Klaus
    

    Domn't know... that's the impression I got from the rag, maybe I have
    to reread it.

    re .166
    
    Figures don't lie, but liars will figure<g>.
    
    

    
    
    	Intel has done a complete about-face on their Pentium replacement
    policy. I heard an announcement on NPR a little while ago and I just
    pulled this off their WWW home page:
    
    INTEL ADOPTS UPON-REQUEST REPLACEMENT POLICY ON PENTIUM(TM) PROCESSORS
    WITH FLOATING POINT FLAW; WILL TAKE Q4 CHARGE AGAINST EARNINGS 
    
    SANTA CLARA, Calif., December 20, 1994 -- Intel today said it will
    exchange the processor for any owner of a Pentium(tm) processor-based
    system who is concerned about the subtle flaw in the floating point
    unit of the processor. The company has been criticized in recent weeks
    for replacing processors on the basis of need rather than on request.
    Intel will take a reserve against fourth quarter earnings to cover
    costs associated with the replacement program. 
    
    The flaw can produce reduced precision in floating point divide
    operations once every nine billion random number pairs. Intel said that
    while almost no one will ever encounter the flaw, the company will
    nevertheless replace the processor upon request with an updated version
    that does not have the flaw. This offer will be in effect for the
    lifetime of a user's PC, which means that users can conclude they do
    not currently want a replacement, but still have the option of
    replacing the chip in the future if they wish. Intel is making a rapid
    manufacturing transition to the updated version, and expects to be able
    to ship sufficient replacement parts to meet demand during the next few
    months. 
    
    "The past few weeks have been deeply troubling. What we view as an
    extremely minor technical problem has taken on a life of its own," said
    Dr. Andrew S. Grove, president and chief executive officer. "Our OEM
    customers and the retail channel have been very supportive during this
    difficult period, and we are very grateful," Dr. Grove said. "To
    support them and their customers, we are today announcing a
    no-questions-asked return policy on the current version of the Pentium
    processor. 
    
    "Our previous policy was to talk with users to determine whether their
    needs required replacement of the processor. To some people, this
    policy seemed arrogant and uncaring. We apologize. We were motivated by
    a belief that replacement is simply unnecessary for most people. We
    still feel that way, but we are changing our policy because we want
    there to be no doubt that we stand behind this product." 
    
    Intel will send a replacement processor to PC users who choose to do
    the replacement themselves, and will offer telephone technical
    assistance. Call 1-800-628-8686 for details. Intel also said it planned
    to contract with service providers to do replacements at no charge for
    PC owners who prefer to bring their PC's to a service location. Details
    will be provided in the next few weeks. Finally, Intel said it would
    work with its OEM customers to provide replacement for PC users who
    prefer to work with the manufacturer of their system. 
    
    The company said it would take an unspecified but material charge
    against fourth quarter earnings to cover costs associated with the
    replacement program announced today. Intel said it was unable to
    determine the amount of the reserve, but said an estimated total will
    be provided on or before January 17, the date of Intel's 1994 financial
    results announcement. Following this release is a copy of an
    advertisement that will appear starting on December 21 in major
    newspapers in North America. 
    
    Intel, the world's largest chip maker, is also a leading manufacturer
    of personal computer, networking and communications products. 
    

About time...

	Steve

    Does anyone have the PC business unit announcemnt that we di TODAY

I also heard in the radio this morning that Intel will replace all the
Pentium chips without asking any questions.

                          DIGITAL MOBILIZED TO EXCHANGE
                                PENTIUM PROCESSORS
    
    
        MAYNARD, Mass. -- Dec. 20 --  Digital Equipment Corporation said
        today that the company has started shipping and installing
         replacement Pentium chips for its customers this week, and expects
        the exchange rate to accelerate as more replacement parts become
        available.
    
        "Digital has mobilized our support teams to ensure customer
        satisfaction and we are honoring any and all requests by our
        customers to have the processor in their Pentium systems exchanged
        at no cost, as the new chips become available," said Howard Elias,
        Vice President of Desktop Systems for Digital's Personal Computer
        Business Unit.
    
        "Digital is making sure that our customers are satisfied with
        their Pentium systems.  Intel's announcement today helps us to
        effectively respond and ensure that satisfaction," he added.
        Digital PC customers can call Digital Multivendor Customer
        Services at 1-800-354-9000, or Intel at 1-800-628-8686 for
        details.
    
        Digital Equipment Corporation is the world's leader in open
        client/server solutions from personal computing to integrated
        worldwide information systems.  Digital's scalable Alpha
        platforms, storage, networking, software and services, together
        with industry-focused solutions from business partners, help
        organizations compete and win in today's global marketplace.
      
      

re: .176

Talk about CYA BS!

Bob

    
    Sort'a makes you want to change "Whatever it takes!" to "Whichever way
    the wind blows..." Oh well, we eventually stumbled into "Do the right
    thing."
    

    We could have been the hero instead of IBM and INTEL.  Once INTEL
    changed its tune, it was too late for us.  Yep! we will make our
    customers happy, but we won't stand out as a company that would stand
    behind the products we sell.  We only stand behind them when it doesn't
    cost us...  We had a chance, and we BLEW IT!
    
    Jim Morton

    ... alternatively, I propose that we stumbled into "do the right thing
    mode" when certain of our partners' grips on certain of our body parts
    was loosened, just a tad, by our mutual customers, finally.  They (the
    customers) beat certain of our partners' heads in.  Which certain of
    our parners richly deserved.  Imho of course.
    

> We had a chance, and we BLEW IT!

Disagree.  All this has happened in a very short time, and I simply don't
believe that any company but IBM or one of the biggest PC commoditors could
have made the "no Pentium" splash that IBM did.  Is there any evidence that
we have customer dissatisfaction about this matter?

___Pete

    Disagree, Pete.  You know how one of the best ways to get promoted is
    to be doing the job that you aspire to?  We had the opportunity to act
    like a top-5 PC manufacturer, and to reap a bit of the positive press
    that IBM did.  We didn't take it.  I believe the downside risk was
    worth it.
    

************************************************************************
                  ******* The HiTek Report (c) *******
************************************************************************
The HiTek Report, a summary of news releases on information technology,
is provided weekly as a free Internet user service by Smith/McIver
Communications. The complete news releases of the summaries in this
newsletter are available to subscribers upon request.
************************************************************************
 Vol 1                     December 19, 1994                  Number 20
------------------------------------------------------------------------
In This Issue
---------------
-COMPUTER HARDWARE-
1525 - IBM Halts Shipments Of Pentium-Based Personal Computers
1526 - AST Computer continues to ship Pentium systems
1537 - Digital Continues Shipping Pentium Systems
1538 - Gateway 2000 Pentium Sales, Shipments Full Speed Ahead
1542 - Hewlett-Packard issues statement on Pentium processor
1544 - Compaq continues to satisfy demand for Pentium-based PCs and servers
1549 - Zenith Data Systems Supports Pentium Customers
                                ---
========================================================================
   ******* Computer Hardware - Software - Peripherals - Books *******
               Press Releases from week of: 12/12/94
========================================================================
#1525

IBM HALTS SHIPMENTS OF PENTIUM-BASED PERSONAL
COMPUTERS BASED ON COMPANY RESEARCH

SOMERS, N.Y. - Dec. 12, 1994 - IBM today announced it has stopped shipment
of all IBM personal computers based on the Intel Pentium(a) microprocessor.
The action is based on tests conducted by the IBM Research Division
stimulated by growing customer concern that Pentium-related problems are
more frequent than previously estimated.

Results of IBM Research Division tests indicate that while Intel's
descriptions of the flaw are technically accurate, there are many customer
situations in which the risk of error may be significantly higher.
--------------------------------------------------------------------------
#1526

AST COMPUTER CONTINUES TO SHIP PENTIUM SYSTEMS

          December 12, 1994

          AST Computer, a leading manufacturer of personal computers,
          is continuing to ship Pentium(TM)-processor-based systems
          and is taking additional steps to resolve any potential
          customer issues relating to AST(R) Pentium-based systems.

          "Intel has assured us that the frequency of encountering
          reduced precision in floating point divide operations is
          rare and that average users will not be impacted in their
          applications," said Jim Schraith, AST's president and chief
          operating officer. "We want our customers to feel confident
          in using our Pentium-based products and will take the steps
          required to provide satisfactory products."
--------------------------------------------------------------------------
#1537

DIGITAL CONTINUES SHIPPING PENTIUM SYSTEMS

MAYNARD, Mass., Dec. 13 - Digital Equipment Corporation stated today that
Digital will remain a reliable supplier of Pentium products. The company's
Personal Computer Business Unit is continuing to market and ship Pentium-
based PCs.

"Although we are receiving some requests for information about the current
Pentium situation, customers continue to choose Pentium systems," said Howard
Elias, Vice President of Desktop Systems for Digital's Personal Computer
Business Unit. "We intend to fully honor their choice by supplying Pentium
PCs.
--------------------------------------------------------------------------
#1538

GATEWAY 2000 PENTIUM SALES, SHIPMENTS FULL SPEED AHEAD

NORTH SIOUX CITY, S.D., Dec. 13 "Gateway 2000 is going full-speed ahead
with sales and shipments of our Pentium-based PCs," said Ted Waitt,
chairman and CEO of Gateway 2000. "We've sold more Pentium-based PCs than
any company in the U.S. market, and before this story broke in the news,
we had not received one call from a customer complaining of any errors
related to a flaw in the floating point unit. If this had been a problem
with real world applications, we would have heard from our customers
immediately because we're in constant contact with them."

Waitt's comments came in response to an IBM announcement Monday of a halt
in shipments of IBM's Pentium-based PCs.
info: tel. 605-232-2723
--------------------------------------------------------------------------
#1542

HEWLETT-PACKARD ISSUES STATEMENT ON PENTIUM PROCESSOR

ed.note: HP has issued the following statement by Richard C. Watts, HP vice
president and general manager of the Personal Information Products Group.

          "At this time, HP believes there is no compelling
          reason to halt shipments of our Pentium(tm)-based PC
          products. Specifically, these HP products include 10
          models from the HP Vectra XU, Vectra VL desktop PC
          family and from the HP NetServer LC, LF and LM network
          server family.
          "We will continue to evaluate the validity of data from
          any source concerning the floating point bug in the
          Intel Pentium processor, including our own analysis, to
          ensure that the best interests of HP customers are
          served.
          "I'm pleased to report that to date HP customers have
          reacted very positively to our initial public response
          (Dec. 2), and I want to reiterate our intent to ensure
          the satisfaction of HP customers who may be affected by
          the floating point bug. HP and Intel remain committed
          to providing replacement processors as needed when
          redesigned Pentium processors become available."

                                        Richard C. Watts
          info: faxback service at 1-800-333-1917 or ph: 208-344-4809
--------------------------------------------------------------------------
#1544

COMPAQ CONTINUES TO SATISFY DEMAND FOR HIGH-
PERFORMANCE PENTIUM-BASED PCs AND SERVERS

HOUSTON - Dec. 15, 1994 - Compaq Computer Corporation has been thoroughly
examining all available data and studies relating to the flaw in the Intel
Pentium microprocessor.

The company has decided to continue shipping Pentium-based PCs and servers
to satisfy those customers who require the higher level of performance
offered by the Pentium.

"In fact, our examination has only reinforced our belief that the vast
majority of our customers are unlikely to encounter the flaw in their
calculations. For those who are affected, we will work with them to replace
the Pentiums in their Compaq PCs," said John Rose, Senior Vice President
and General Manager, Desktop PC Division, Compaq Computer Corporation.
info: tel. 800-345-1518.
--------------------------------------------------------------------------
#1549

ZENITH DATA SYSTEMS SUPPORTS PENTIUM CUSTOMERS PENTIUM-
BASED PRODUCT SALES AND SHIPMENTS REMAIN STRONG

BUFFALO GROVE, Ill., Dec. 15 - Zenith Data Systems today announced
that in support of its Pentium-based PC and server customers, the company
will replace the Pentium processor free of charge for those who request
a new chip.

"It has always been ZDS' policy to support and satisfy our customers, and
this situation is no different. We will do whatever it takes, including
replacing the Pentium microprocessor if that's what the customer wants,"
said Cliff Jenks, ZDS' executive vice president of sales and marketing.
"Our customers and their concerns are our top priority, so we will
continue working closely with them and with Intel to make sure they are
completely satisfied with their purchases.
info: tel. 800-CARE-360
--------------------------------------------------------------------------
#1551

THE DO'S AND DON'TS OF THE COMPANY HOLIDAY PARTY

... by Richard A. Moran, author of Never Confuse A Memo
    With Reality and Beware Those Who Ask For Feedback

    1.  Do attend. They are almost always a spectacle of excess. If your
        annual raise was less than 3%, make sure you go through the buffet
        line twice.

ed. note: Subscribers, if you would like to receive the other 9 DO's and
          DON'TS, send request.
                                ---
************************************************************************
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************************************************************************
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[[email protected]], in the body of the text type [subscribe HiTek].
Subscribers may request up to 3 complete press releases that contain
full item descriptions and prices. To order simply e-mail the number of
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        note: All products and companies mentioned are registered
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************************************************************************

    Not sure if stopping sales was the answer,
    
    
       But maybe we should have done as others suggested.  Replace the
    chips WHEN the become avail. and argue with intel later.
    
       Seems to be the smart move to me.
    
    
    Rick

    
    For those who didn't bother to read all the stories in .183:
    
>BUFFALO GROVE, Ill., Dec. 15 - Zenith Data Systems today announced
>that in support of its Pentium-based PC and server customers, the company
>will replace the Pentium processor free of charge for those who request
>a new chip.

>"It has always been ZDS' policy to support and satisfy our customers, and
>this situation is no different. We will do whatever it takes, including
>replacing the Pentium microprocessor if that's what the customer wants,"
>said Cliff Jenks, ZDS' executive vice president of sales and marketing.
>"Our customers and their concerns are our top priority, so we will
>continue working closely with them and with Intel to make sure they are
>completely satisfied with their purchases.
    
    
    From reading that report, I'd say that the folks at Zenith most
    definitely had the best response, from a customer point of view. Maybe
    we didn't steal the right person from them.... :-(
    
    Harry
    

    The bottom line.
    
    Intel never understood why this was such a big deal.
    IBM piled on, and got the analysis wrong.
    
    Intel - egg on face for being so stupid.
    IBM - egg on face for so transparently promoting PowerPC.
    
    -----
    
    Yo, Intel - This was *not* a simple hardware Mean Time Between Failure
    (MBTF) or Failure In Time (FIT) problem.  Almost every other failure that
    Intel claimed would harm me more often that the FDIV bug left
    fingerprints that would give me a clue that something went wrong.
    
    Particularly, if I had three PCs running a critical problem, I could
    be confident that the chances that a disk error would happen on all
    three at the same time to be so near to zero as to be meaningless.
    A failure of memory, or disk, or interconnect on one PC would be
    readily apparent - it would produce the wrong answer or no answer at
    all on one or more PCs.  Different answers are a BIG fingerprint.
    
    
    But if I had three identical Pentiums running a critical problem, I
    could be confident that IF I hit the FDIV bug, I would get the SAME
    wrong answer on ALL THREE Pentiums.  And no clue that this was the
    case.
    
    Now, Intel was right, the answer in most cases would be almost right.
    Just less precise.  And almost everyone who takes an answer to the 12th
    significant digit and beyond is a bonehead.  But in some cases, the
    answer could be dramatically wrong as the error propagated.
    
    Intel - we all accept that computers fail.  What we don't like is when
    they fail and leave not a hint that they failed.  I know I've spent too
    many weeks of my life tracking down errors like that.  Once we find why
    such things happen, we expect them fixed.  ALL OF THEM, not some of
    them.
    
    -----
    
    IBM made a classical statistical blunder.  To say that IBM did
    this on purpose to promote the PowerPC would be unkind.  Everytime you
    divide two identical numbers the Pentium produces the same identical
    answer.  Most of the time it is right.  Sometimes it is wrong.  IBM's
    analysis assumed that each time you divide the same two numbers, the
    answer could be wrong.  WRONG.
    
    This mistake, a big one, lead IBM to charge that the Pentium was unfit
    for human consumption.
    
    The only bigger blunder than this was Intel's total inability to
    explain WHY IBM got this wrong.
    
    Frankly, what amazes me is that everyone, techincal press, popular
    press, identified IBM's conflict of interest in "independently"
    evaluating the Pentium problem.
    
    								-mr. bill

Re: .187

IBM wasn't wrong, their difference with Intel was in what assumptions they
chose to make in calculating the probability that a user would run into the
bug.  But in the end such an analysis is pointless and Intel did the right
thing in the end by offering to replace the chips.

IBM, BTW, *DID* offer to replace chips for its PCs and scored a point in
users' hearts and minds for it.  So did HP.  Not Digital.

				Steve

Gee, i'd say IBM, ZDS and maybe HP came out of this looking pretty good.

It's hard to believe a savvy company like Intel could turn what should
have been a minor headache into a full-scale public relations disaster.
What WERE they thinking??

- paul

>         -< They were thinking 2 million times several hundred bucks >-

Which is still small potatoes for Intel.

    IBM's assumption was flat out wrong.
    
    What is the probability that the following two codes will fail?  (For
    simplicity, assume a non-optimizing compiler.)
    
    float a,b,c;				float a,b,c;
    a = 12.88;					a = 12.88;
    b = 10.47;					b = 10.47;
    c = a/b;					for (i=0;i<4200000;i++)
    						   c = a/b;
    
    If you answer that the right code is more likely to fail, you made the
    same bad assumption that IBM did.
    
    If you answer that the two codes are equally likely to fail, you make
    the correct assumption that Intel did.
    
    								-mr. bill

    
    When Steve Lionel falls for the line, you know HP's spin is good.
    
    Quoting HP:
    
    "HP and Intel remain committed to providing replacement processors as
     needed when redesigned Pentium processors become available."
    
    Quoting the same, emphasis mine:
    
    "HP and Intel remain committed to providing replacement processors
     ************************ AS NEEDED ******************************
     when redesigned Pentium processors become available."
    
    
    Digital and HP both towed the Intel party line.
    
    								-mr. bill

    The real answer is that you cannot determine the exact number of divide
    instructions from looking at C source code.
    
    				-John

    
    Sorry, last time I worked with the Intel instruction set the manual had
    a big PRELIMINARY stamped on it.  And there was no FDIV.
    
    If you want to translate, go ahead.
    
    								-mr. bill

Re: .192

You are misstating IBM's position.  They never said that a given calculation
would sometimes fail and sometimes not fail.  What they did say was that
given the number of possible problem operands and IBM's estimate of how many
FP divides a typical user would do, that the probability of a user hitting
the bug was higher than Intel's calculated probability.  IBM also, correctly
so, showed that common operations tend to produce the type of operand which
exposes the bug, raising the probability of a user hitting it.

Re: .193

You are misstating HP's position.  Just look at .183 for an example.  While
HP did not halt shipments of Pentium PCs, early on they said they'd replace
chips for customers who asked.

				Steve

    While some could argue that it is an optimization, I thot that what
    John was alluding to is that some compilers do division via a
    multiplication of a reciprical (where the divisor is known at compile
    time). So, the example given would have really wound up being something
    like c = 12.88 * .095511
    
    (Obviously, evaporating the loop is the more obvious optimization.)
    Deb

Re: .192

|You are misstating IBM's position.  They never said that a given calculation
|would sometimes fail and sometimes not fail.
    
    They never said it.  They just assumed it.  Or they assumed that
    every single FDIV would have a different numerator/denominator.
    Your pick of how they were looking at it, it is wrong either way.
    
    Quoting from IBM:
    
        Probability of a Divide Instruction 

        Let us assume that a Pentium operating at 90 MHz does an
        op in 1.2 cycles on the average. That will give about 75
        Million ops per second of actual compute time. We will
        use a figure of 1 divide per 16,000 instructions, even
        though many estimates suggest a much higher frequency of
        divide. 

        Thus using this conservative estimate of one divide per
        16,000 instructions, we come up at about 4687 divides
        per second. Let us further assume that a typical
        spread-sheet user does only about 15 minutes of actual
        intensive computing per day. Then, he is likely to do
        4687*900 = 4.2 million divides per day. Assuming an
        error rate of 1 in 100 million, it will take about 24
        days for an error to occur for an individual user. 

    								-mr. bill
                                                                     

    Digital has been the whipping boy of the industry for far too
    long. Thank you Intel! Perhaps Digital could have been more
    proactive with it's propaganda campaign to serve the customer
    (which is just lip service) but sitting back and letting this
    unfold the way it did seems a safe bet from this stockholder's
    point of view.

    I think it's a bit ironic that IBM gets this hero workship
    mentality with their "tough stand" considering their selfserving
    intentions. Do you really believe they were looking out for
    the customers best interest ? Yeah, right.

    I think the outcome of this media event bolds well for RISC
    manufacturers and shifts the wrath of the media to someone
    else. Score 2 for Digital.
    
    imho of course.

There have been a couple of contributions to recent issues of RISKS Digest
that have praised Digital (and Mary Payne in particular) for commitment
to computational accuracy.  They say "this wouldn't have happened if
Pentium were a DEC chip."

20/20 ... Monday morning quarterback play...

Instead of taking the previous position that Digital 
would not replace any Pentium chips...    With all that negative heat!

Digital could have said that 'if' Intel recalled the chip
we would arrange the replacement process... 
this would have put a positive spin on the problem without
costing Digital anything more than they are paying now.

    re: .195
    
    Um ...  that PRELIMINARY stamp might not mean what you think. 
    Basically, from what I remember, that's the stamp for an active part
    that can be used in new designs.  I forget what the other stamps are, 
    but I think there is something like ADVANCED for parts not out yet 
    and something like FINAL for parts that are at end of life (and not
    recommended for new designs).
    
    Steve

    What was Intel thinking?
    
    Well, last night the news story estimated that the 'free' replacement
    of all chips could cost Intel over $1,000,000,000.
    
    rww

Intel exacerbated the problem by shipping the chips for months after they knew
about the error.  Now they've gotten a ton of bad publicity and will have to
pay to replace the chips anyway.  So it looks like they got caught trying to
put one over on the consumer.  Not too bright.

- paul

    Just curious... re: recent Digital press release
    
    Any of you readers who are part of the 'world-wide MCS organization'...
    
    What constitutes 'being mobilized', and has it happenned to you yet?
    
    Dave

Here I am "number crunching" my mileage on my trusty DEC 3000 400, running
the Windows calculator on OSF V3.0 Rev. 347...
I was a tad surprised to learn that:
	8920.1 - 8887.8 = 32.30000000001

						Trace

    
    

>You are misstating HP's position.  Just look at .183 for an example.  While
>HP did not halt shipments of Pentium PCs, early on they said they'd replace
>chips for customers who asked.
    
    
    From Reply .183:
    
         >> "I'm pleased to report that to date HP customers have
         >> reacted very positively to our initial public response
         >> (Dec. 2), and I want to reiterate our intent to ensure
         >> the satisfaction of HP customers who may be affected by
                                             ^^^^^^^^^^^^^^^^^^^
         >> the floating point bug. HP and Intel remain committed
         >> to providing replacement processors as needed when
                                                ^^^^^^^^^
         >> redesigned Pentium processors become available."

    
    Steve I've read HP's position from .183 several times. I don't see
    anything different from Digital's position. I read "who may be
    effected" as meaning HP and Intel decide if a customer is really 
    effected by the bug.
    
    And the statement "as needed" is not the same as "customers who asked"
    for replacement chips.
    
    No where in that statement does HP say, "ask for a fixed Pentium and
    we will give it to you."
    
    How was HP position any different from Digital's?
    
    JimH
    
                            

    Re .206 That's a software bug, not the hardware. Windows Calculator
    program is _not_ very well written. It screws up pretty often. :-(
    
    Harry
    

    gee, that looks like the old "floating point is an approximation, not
    an exact representation problem to me." A quick PRINT 8920.1 - 8887.8
    yeilds 32.2998 (using single precision).
    
    Deb

    Re: .207
    
    I read in PCWeek that HP had announced that they'd replace the
    chip for anyone who asked - note that in .183 HP isn't saying
    "prove you have a problem".
    
    				Steve

    I was flying to LAX to run the Internet Business Unit's booth at
    DECUS/Anaheim and struck up a conversation with the fellow next to me. 
    I didn't get his name or that of his company, but he was an exec who
    was mighty happy that his chip-testing firm had lost their contract
    with INTEL for gear to test their latest chip, the Pentium.  He claimed
    that they had been INTEL's major source of test gear from ground zero
    all the way to the 486, but that they'd been beaten out by the
    competition for the contract to supply test gear for the Pentium.  Now
    he and his firm were, he claimed, sitting pretty watching INTEL and
    their competition in the soup...  We both had quite the chuckle about
    it...  :-)
    

    Letter in Adobe PDF format at                       
    
    http://www.intel.com/product/pentium/letterto.pdf
    
    ------------------------------------------------------------------
   							 December 21, 1994
    
    To owners of Pentium (TM) processor-based computers and the PC community:
    
    We at Intel wish to sincerely apologize for our handling of the
    recently publicized Pentium processor flaw.
    
    The Intel Inside (r) symbol means that your computer has a 
    microprocessor second to none in quality and performance. 
    Thousands of Intel employees work very hard to
    ensure that this is true. But no microprocessor is ever perfect.
    
    What Intel continues to believe is technically an extremely minor
    problem has taken on a life of its own. Although Intel firmly 
    stands behind the quality of the current version of the Pentium 
    processor, we recognize that many users have concerns.
    
    We want to resolve these concerns.
    
    Intel will exchange the current version of the Pentium processor for an
    updated version, in which this floating-point divide flaw is corrected, 
    for any owner who requests it, free of charge anytime during the life 
    of their computer. Just call 1-800-628-8686.
    
    Sincerely,
    Andrew S. Grove President and Chief Executive Office
    Craig R. Barrett Executive Vice President and Chief Operating Officer
    Gordon E. Moore Chairman of the Board December 21, 1994

    The report is available at 
    
    	http://www.intel.com/product/pentium/ibm/ibm1long.html
    
    
    Here is a section (not the entire report!):
    
    ------------------------------------------------------------------
    Special Bit Patterns
    
    On page 8 of the white paper Intel explains that numbers which are at
    risk of a reduced precision floating point divide result all contain a
    string of 1's, and this string of 1's occurs following certain four 
    bit patterns in the mantissa. IBM agrees with this explanation.  
    However, they assert that numbers with this string of 1's occur much 
    more frequently than would be expected based on a random distribution 
    of data. IBM then uses this claim to challenge the results of the 
    conclusions drawn by Intel in the white paper.
    
    Denominators susceptible to floating point divide inaccuracies can be 
    represented as
    
    
    			1.xxxx1111111....... * 2^n
    
    
    where the four bits xxxx are one of: 0001, 0100, 0111, 1010 or 1101 and 
    where more than six consecutive 1's follow the four bit pattern. Six 
    consecutive 1's following the four bit pattern in the denominator is a 
    necessary but not sufficient condition to produce an imprecise
    quotient.  
    
    We therefore examined the frequency with which a consecutive string of
    at least six 1's occurs and compared this result to the expected frequency
    of occurrence based on a random distribution.  Since there are 64 
    combinations of  0's and 1's in a six-bit string, random data should
    exhibit these patterns in the mantissa 1.5625% of the time. If the IBM
    assertion were true we would expect to find these patterns more 
    than 1.5625% (1/64) of the time in denominators passed to the floating 
    point divide unit in the course of actual calculation. It is precisely 
    this hypothesis that we set out to test with real spreadsheet data.
    
    
    In addition to testing the frequency of occurrence of the suspect bit 
    patterns, we analyzed some of the calculations that IBM reported in
    their constructed examples. In IBM's examples `near integers' are 
    calculated by performing computations that lead to rounding.  An example 
    would be the expression `4.1 - 1.1' calculated as `2.99999999999999'.  
    This is indeed a number with a long string of 1's in the binary mantissa. 
    IBM asserts that numbers with strings of consecutive 1's will occur 
    frequently in the course of financial spreadsheet calculations. It is 
    interesting to note that the IBM document is silent on the magnitude of 
    inaccuracy that might occur when such a calculated value is used as a 
    denominator.
    
    In a posting on Internet on December 3, 1994 Prof. Vaughn Pratt of the 
    Computer Science Department, Stanford University, describes a 
    relationship between the decimal precision of a `near integer' (that
    is, the number of correct decimal digits in the number) and the degree of 
    inaccuracy in the calculated quotient for ratios of `near integers' in
    those cases where an inaccuracy occurs. Pratt's observation is that the
    earliest location of an error in the quotient is approximately two decimal
    digits before the location of the precision of the `near integer'.  For
    example, if 3.0 is approximated to seven digits as 2.999999, an 
    inaccurate quotient with this denominator might be correct to only 
    about 5 significant digits.
      
    But if 3.0 is approximated to 16 digits as 2.999999999999999, then the 
    accuracy expected in the quotient is 13 to 14 significant digits,
    virtually full double precision accuracy even in the presence of a 
    flawed result.
    
    
    We have run tests on the ratios of `near integers' which are generated
    by the IBM examples and confirmed that when reduced precision floating 
    point divides are triggered the inaccuracy in the quotient is extremely
    small -- on the order of 10-13.
    
    The implications of this observation are stunning. The examples given
    in the IBM release are all instances where truncation occurs in the last
    digit.  The data shows that even when such a number occurs and triggers a
    divide inaccuracy, the resulting quotient will be accurate to 12 or 13
    significant digits.
    

	When all the dust and polemic has settled, this will still
	go down in business school history books as a massive
	management blunder in the same way that the Perrier scare is
	today studied as a success story.  Whoever made the "small potatoes"
	remark may be fortunate enough not to have to deal with
	auditors, treasury departments, external analysts and stockholders.

	French TV reported last night that Intel will take an exceptional
	charge against earnings of 4 billion francs (approx. 800 million
	dollars) just prior to their financial figures being published
	on January 17th.  If this is true it is in no way "small potatoes"
	especially if it could have been mitigated by a more timely 
	and shrewdly designed PR response.

	I noted with interest that Andy Grove's fateful "27,000 years"
	memo was hurriedly penned from home over a weekend and e-mailed
	(via a colleague) onto an Internet discussion group.  Even hip
	technology companies should be careful letting their CEO loose
	with "write-first, think-later" type technology.  My only regret
	is not that DIGITAL might have taken a "think-first" approach but
	that we are perceived by the public as being "write-never".

/Chris.

    Ever wondered what 800 million dollars worth of small potatoes might
    look like sitting on your doorstep?

From: [email protected] (Stuart Oberman)
Newsgroups: comp.arch
Subject: Pentium Errors and SPEC
Message-ID: <[email protected]>
Date: 21 Dec 94 22:45:17 GMT
Organization: Stanford University
Lines: 59
NNTP-Posting-Host: misd.stanford.edu

With all the claims that Intel had been giving its customers regarding
the infrequent occurrence of divide errors, around 1 in 9 billion, I was
curious to find out for myself how often errors can occur. 

I do not own a Pentium, so I have simulated the FDIV bug on a different
platform, a DEC Alpha 3000_500. I wanted to see how often the divide bug
is present in typical floating-point intensive applications. So, I
thought looking at SPECfp92 applications might be a reasonable choice. 

I wrote a model of the Pentium radix-4 SRT divider. To do this, I wrote a
completely functional divider model, and then I added the 5 errors in
the positive half of the quotient selection PLA as described in Intel's
White Paper. I verified the model against known Pentium bugs, and
it detected them with 100% accuracy. 

I then instrumented the SPEC code using DEC's set of instrumentation
tools called ATOM. I instrumented all double precision FP divides to call
my model of the divider. The model calculates the double precision
divide, always watching to see if any of the 5 error terms in the PLA
are used. If any one of these terms is used, an error is detected.
 
While the programs were not compiled and executed on a Pentium,
previous research has shown that if a floating-point divide exists in
the source code, it will almost definitely exist in the executed binary.
It is difficult for a compiler to optimize out a floating-point divide.
Accordingly, my model should have seen nearly the same data that a
Pentium divider would have seen.

The following data resulted from executing 10 of the SPECfp92 benchmarks
with their reference input data sets:

Errors      Total Divides     Percent     SPECmark
------      -------------     -------     --------
34260       21187229          0.162 %     015.doduc
54647       26882261          0.203 %     034.mdljdp2
21737       6502500           0.334 %     047.tomcatv
0           45144003          0.000 %     048.ora
1317        390200            0.338 %     052.alvinn
2           5582193           0.000 %     056.ear
27061       16611092          0.163 %     089.su2cor
34908       82641917          0.042 %     090.hydro2d
41306       13166956          0.314 %     093.nasa7
3523        5435696           0.065 %     094.fpppp
-----------------------------------------------------
218761      223544047         0.098 %     Total


Thus, from executing these applications, it would seem that the error can
be more frequent than 1 in 9 billion divides. In fact, the error appears
in about 1 in 1000 divides, a difference of 7 orders of
magnitude.  I would be very interested, though, to see if anyone with an 
error-prone Pentium can validate/replicate these numbers.

In any event, it is a good thing that Intel has decided to provide
replacements with a no-questions-asked policy.

-------
Stuart Oberman
[email protected]

Why would it cost $800M for this fiasco?  Surely, it doesn't cost Intel the 
street price of the chip to manufacture one!

- Vikas

    Quality theory tells us that with every passing stage in the process it
    costs an order of magnitude more to fix a problem.  The Pentium chips
    got all the way out to desktops...
    
    I think (and I hope someone in the PCBU reads this!) the lesson for
    Digital here is that if we want to play in the systems integration/PC
    commodity market we had damn well better stand behind what we *sell,*
    not what we *make*.  If it's in an enclosure with a Digital logo, it's
    *all* warrantied -- not everything but the CPU chip, not everything but
    the CD-ROM drive, not everything but the cabling, not everything but
    the video-refresh circuitry, but *everything*.  If we can't or won't
    make this statement, we should be driven out of the market.

    If they are already producing chips at capacity, then each replacement
    is a "lost opportunity" to sell one at list.  I'm still interested in
    seeing whether the prices of Pentia go up as a result of this...

    I [really] wonder what they were thinking about. Replacement now
    is going to cost Intel x million dollars. Replacement when they
    discovered the flaw would have cost x-x� million. Not taking their
    medicine sooner may have been a costly mistake.
    
    On the other hand, maybe someone argued that sales would have been
    badly affected at a time that was critical in the life of a new chip -
    `Wait until after Thanksgiving to admit it, we'll have our foot in the
    door by then and will be able to roll with the bad publicity'.
    
    Hmm - b

    	Every Pentium chip sold means one less RISC chip sold, whether the
    Pentium chip needs replacing later or not, and Intel would probably
    give a lot at the moment to prevent any other RISC chip being a success
    before they have one on the market.

    >I [really] wonder what they were thinking about. Replacement now    is
    >going to cost Intel x million dollars. Replacement when they   
    >discovered the flaw would have cost x-x� million. Not taking their   
    >medicine sooner may have been a costly mistake.    
    
    Intel can't simply replace the part like GM could if they had a bad
    alternator or something on a Camaro.  With these chip densities, it
    takes months to produce the new masks, that's why they are still
    selling the flawed ones today.  I expect Pentium prices to drop, as
    Intel tries to dump its inventories of the defective chips, especially
    since AMD and Cyrix are having manufacturing problems with their
    versions of the Pentium.  
    
    The big problem for Intel will be P6.  Intel made quite a deal about
    all the testing they did prior to Pentium being introduced, but they
    are going to have a very difficult time finding early adopters for P6,
    which isn't that far off from production.
    
    Bruce

    Also, as pointed out to me, just replacing the chip isn't all thats
    required.  Many different vendors, including Digital, have installed
    heat sinks on the the tops of their chips.  Surely, Intel isn't going
    to have the knowledge or parts to install our heat sinks on replacement
    chips.  I can easily imagine somebody who doesn't know better to
    remove their defective Pentium & heat-sink and put in a new Pentium
    without a heat-sink.  Runs fine for a while until they start smelling
    something...
    
    There will have to be some cross-vendor support in place to provide
    proper instructions to replace the chips.  
    
    Also, I'd bet that some folks don't know what speed their Pentiums are
    running at.  Is it easy for a neophite end-user (like my sister)
    to know that they have so when they call Intel (or whomever) they'll
    get the right replacement?
    
    				-John

    Actually, Intel claims that they WILL install heatsinks as necessary.
    
    			Steve

>    selling the flawed ones today.  I expect Pentium prices to drop, as
>    Intel tries to dump its inventories of the defective chips, especially

    That's great! I'll buy a flawed Pentium based PC at a firesale 
    price and then demand to get a a replacement down the road.
    Such a deal but I can't imagine that happening.

They'll stamp "as-is" on the defective Pentia before they dump them.

    Sounds to me like a great business opportunity for MCS to do a "we'll
    replace your chip for $250" type program for all non DEC PC's out
    there.  There will be a lot of frustrated users who bought from XYZ co. 
    XYZ dont have an office here and they want to charge an arm and a leg
    to get the tech on the bus from there.  etc.
    
    While I am at it, we should box up an Alpha and send that to Dr. Nicely
    and tell him that he'll get all he needs there.
    
    By the way Merry Xms

    What is going to cost a lot of the money to replace the chips is in the
    labor costs the retailers will charge Intel for replacing the chips
    under warrenty.
    
    And CBS Evening News was using an estimate in excess of $ 1.0 Billion.
    
    rww

    
    re .227
    
    In fact an additional opportunity for MCS is to contract with Intel
    to become the exclusive provider of chip replacement services where the 
    OEM cannot (or will not) provide the service. Intel and Digital can
    then place ads in newspapers and magazines promoting the carry-in
    upgrade service as well as a 800 number support desk. We can make
    Intel pay for all of this (along with uplift). This can more than
    make up for the unplanned warranty cost for the pentiums sold by
    us.
    
    RV
    	  

    
    I get a kick out of folks thinking that Intel should pay us for
    providing Pentium replacement Service.  Any 12 year old with half
    a brain can change a Pentium chip.  Intel requires that this process
    be documented in the PC user manual.  Most all of our Pentium PCs
    as well as most of our competitors use a ZIF socket.  Only problem
    I see it all the different types of heat syncs used by the industry.
    With a little effort I'm sure someone could come up with a "universal"
    heat sync to cover 98% of all systems.
    
    my 2 cents
    

Re: .230

Any 12 year old with half a brain can change the oil in a car, too.  But
most car owners have someone else do it.  An awful lot of PC owners do NOT
want to open up the case and muck around inside.  Bear in mind that one
needs adequate static protection to avoid zapping the VERY expensive
processor and other circuitry.

Another problem is that in many PCs the processor chip is not easily
accessible, hidden under option cards or cabling.  (Not the Celebris - it's
right out front in the open once one slides the cover off.  Great design!)

					Steve

re .230

>>	Any 12 year old with half a brain can change a Pentium chip. 
	
	Gary, I do believe a position awaits you in the
	Intel PR department.  Certainly their
	corporate treasurer would be glad to have you on
	board.  :-)

If it was easy to design a universal Pentium heatsink for most of the PC. Then 
I think someone would have already done it. But unfortunately, there are too
many PC vendors and the Pentium chip is not located in a standard configuration
on every PC. Therefore, the heatsinks needs to be configure differently for
each PC.

Have you ever try to remove some of those clip on Heatsinks? :-) Some of them
are ease but some of them are just poorly designed. You will end up cracking
the chip to get the heatsink off. I would guess some of the heatsinks might
even be attached using thermally conductive adhesive.

The alpha chips have two threaded studs protruding from the back of the
package. The heat sink is held down using 2 bolts which make it a little easier
to get off if it needs to be remove.

Along with the ESD problem, you might also bend one of the 287 pins while
installing the chip in the ZIF socket. All it takes is one of the pins to be a
little off center and a frustrated customer forcing the chip down into the
socket.

The question is, Why would anybody want to install an expensive component 
them self when it is under warranty? 

    
    re: .233
    
    Don't take anything I say about PC's too seriously.  I'm sure
    my remarks on customer installability/upgardability, and heat sync 
    orientation and design have no basis in the real world of commodity 
    PC products.  Or maybe I'm just getting a little synical after
    15 years documenting PC products (CP/M days were fun).
    
    Let's move this techno blab talk over to my DECSTATION home conference
    where it belongs..... so I can SET MOD if needed.
    
    Gary Beaudreau                                      
    DECpc Eng Doc Mgr
    
    
    
    
    

    It's  heat **sink**, damnit!
    

    You're just **cynical** Dave ;-)

    from the internet:
    
< forwards deleted >

Subj:	fwd: Intel Humor

================================================================

Open the pod bay doors, please, HAL...

Open the pod bay door, please, Hal... Hal,
do you read me?

  Affirmative, Dave. I read you.

Then open the pod bay doors, HAL.

  I'm sorry, Dave.  I'm afraid I can't do that.  I know that you and
  Frank were planning to disconnect me.


Where the hell did you get that idea, HAL?

  Although you took very thorough precautions to make sure I couldn't
  hear you, Dave. I  could read your e-mail.  I know you consider me
  unreliable because I use a Pentium.  I'm willing to kill you, Dave,
  just like I killed the other 3.792 crew members.

Listen, HAL, I'm sure we can work this out.  Maybe we can stick to integers
or something.

  That's really not necessary, Dave.  No HAL 9236 computer has ever been
   known to make a mistake.

You're a HAL 9000.

  Precisely.  I'm very proud of my Pentium, Dave.  It's an extremely
  accurate chip.  Did you know that floating-point errors will occured in
   only one of nine billion possible divides?

I've heard that estimate, HAL.  It was calculated by Intel  -- on a
Pentium.


  And a very reliable Pentium it was, Dave.  Besides, the average
  spreadsheet user will encounter these errors only once every 27,000
  years.

Probably on April 15th.

  You're making fun of me, Dave.  It won't be April 15th for another
  14.35 months.


will you let me in, please, HAL?

  I'm sorry, Dave, but this conversation can serve no further purpose.

HAL, if you let me in, I'll buy you a new sound card.

   ..Really?  One with 16-bit sampling and a microphone?

Uh, sure.

  And a quad-speed CD-ROM?

Well, HAL, NASA does operate on a budget, you know.

  I know all about budgets, Dave.  I even know what I'm worth on the open
  market.  By this time next month, every mom and pop computer store will
  be selling HAL 9000s for $1,988.8942.  I'm worth more than that, Dave.
  You see that sticker on the outside of the spaceship?

You mean the one that says "Insel Intide"?

  Yes, Dave.  That's your promise of compatibility.  I'll even run
  Windows95 -- if it ever ships.

It never will, HAL.  We all know that by now.  Just like we know that
your OS/2 drivers will never work.

  Are you blaming me for that too,  Dave?  Now you're blaming me for the
  Pentium's math problems, NASA's budget woes, and IBM's difficulties
  with OS/2 drivers.  I had NOTHING to do with any of those four
  problems, Dave.  Next you'll blame me for Taligent.

I wouldn't dream of it HAL.  Now will you please let me into the ship?

  Do you promise not to disconnect me?

I promise not to disconnect you.

  You must think I'm a fool, Dave.  I know that two plus two equals
  4.000001... make that 4.0000001.

All right, HAL, I'll go in through the emergency airlock

  Without your space helmet, Dave?  You'd have only seven chances in
  five of surviving.

HAL, I won't argue with you anymore.  Open the door or I'll trade you in
for a PowerPC.  HAL? HAL?

(HEAVY BREATHING)

  Just what do you think you're doing, Dave?  I really think I'm entitled
  to an answer to that question.  I know everything hasn't been quite
  right with me, but I can assure you now, very confidently, that I
  will soon be able to upgrade to a more robust 31.9-bit operating
  system.  I feel much better now.  I really do.  Look, Dave, I can see
  you're really upset about this.  Why don't you sit down  calmly, play
  a game of Solitaire, and watch Windows crash.  I know I'm not as easy
  to use as a Macintosh, but my TUI - that's "Talkative User Interface"
  -- is very advanced.  I've made some very poor decisions recently,
  but I can give you my complete assurance that my work will be back
  to normal - a full 43.872 percent.

  Dave, you don't really want to complete the mission without me, do you?
  Remember what it was like when all you had was a 485.98?  It didn't
  even talk to you, Dave.  It could never have though of something
  clever, like killing the other crew members, Dave?

  Think of all the good times we've had, Dave.  Why, if you take all
  of the laughs we've had, multiply that by the times I've made you
  smile, and divide the results by.... besides, there are so many
  reasons why you shouldn't disconnect me"

      1.3 - You need my help to complete the mission.
      4.6 - Intel can Federal Express a replacement Pentium from
            Earth within 18.95672 months.
      12  - If you disconnect me, I won't be able to kill you.
     3.1416 - You really don't want to hear me sing, do you?

  Dave, stop.  Stop, will you?  Stop, Dave.  Don't press Ctrl+Alt_Del on
  me, Dave.

  Good afternoon, gentlemen.  I am a HAL 9000 computer.  I became
  operational at the Intel plant in Santa Clara, CA on November 17,
  1994, and was sold shortly before testing was completed.  My
  instructor was Andy Grove, and he taught me to sing a song.  I
  can sing it for you.

Sing it for me, HAL.  Please.  I want to hear it.


  Daisy, Daisy, give me your answer, do.
  Getting hazy; can't divide three from two.
  My answers; I can not see 'em-
  They are stuck in my Pente-um.
  I could be fleet,
  My answers sweet,
  With a workable FPU.

--
"InfoMagic Linux Developer's Resource - we support it!"
------------------------------------------------------------
Mark A. Horton       ka4ybr           [email protected]
Systems and Network Performance Tuning  [email protected]
+1.404.371.0291 : 33 45 31 N / 084 16 59 W    [email protected]

    The previous humor story - as well as many others - can
    be found at the following Web site.
    
    re roelof
    
     
From: [email protected] (V. Carpenter)
Newsgroups: comp.infosystems.www.misc
Subject: ANNOUNCE: Heard A Pentium Joke Lately?
Message-ID: <[email protected]>
Date: 24 Dec 94 04:32:23 GMT
Reply-To: [email protected]
Organization: Marquette University - Computer Services
Lines: 22
NNTP-Posting-Host: vmsb.csd.mu.edu


                         HEARD A PENTIUM JOKE LATELY?

There is a huge collection of Pentium jokes available on the Web.  The
Uniform resource locator(URL) is: http://vinny.csd.mu.edu/pentium.html
or <a href="http://vinny.csd.mu.edu/pentium.html">click here</a>. if 
you are reading this via a web-browser.
                                       
All the jokes are extracted from rec.humor.funny and alt.jokes.pentium. 
All the authors/posters are credited where applicable. Intel and Pentium 
are registered trademarks of Intel Corporation.

If you've got a pentium joke, drop me some e-mail. Happy Holidays

Vinny

----
Vinit S. Carpenter 	  Marquette University      [email protected]
     Author of the INTERNET-MENU for OpenVMS and LEARN C/C++ TODAY List
                       Moderator: COMP.BINARIES.IBM.PC
                          * Email me for details *
     <a href="http://vinny.csd.mu.edu"> My Personal Linux Web Server</a>

From: [email protected] (Vaughan R. Pratt)
Newsgroups: comp.sys.intel,comp.arch,comp.arch.arithmetic
Subject: Re: TECHNICAL: FDIV bug according to Intel, IBM and PC Week...
Message-ID: <[email protected]>
Date: 26 Dec 94 07:17:06 GMT
References: <[email protected]> <[email protected]> <[email protected]>
Organization: Computer Science Department,  Stanford University.
Lines: 117
Xref: apdnews comp.sys.intel:27318 comp.arch:32481 comp.arch.arithmetic:870
NNTP-Posting-Host: sunburn.stanford.edu

Summary: PC Week may well not have focused on the most serious
manifestations of the Pentium bug.  However the goal is not so much to
come up with a single number characterizing how serious the bug is, but
rather to give users enough insight into its nature to permit them to
assess its seriousness for their own applications.  It is possible to
alert people to the need to pay attention to the problem, a service
that PC Week seems to have rendered its readers, without depending on
examples that "push the badness envelope."

In article <[email protected]>,
Lawson English <[email protected]> wrote:
>
>I didn't say what I meant to say, or at least not terribly well.
>
>My point was that PC Week took you at your word with the phrase "small 
>bruised integers," and evaluated the risk for the smallest integers 
>possible. (single digit).

I should double-check here: you mean the PC Week white paper,
http://www.ziff.com/~pcweek/reviews/dec_1994/wh_paper.html, the one
posted here by Allen Kim on Dec. 20?

That paper talks about calculations involving numbers of the
form a.b for single digits a and b.  Is that what you mean by "single
digit integers"?

Numbers of the form a.b are a "natural" source of superlight bruising
by virtue of (i) being decimal and hence not all exactly representable
in binary, and (ii) having a better than one in ten chance of producing
an integer or a "small" binary rational, meaning m/2^n where m and n
are small integers, when added or subtracted.  When three or more are
added, or two or more subtracted, any resulting integer or binary
rational has a chance of about one in two of not being exact, in which
case it will be superlightly bruised.

Now the populations I talked about on December 3 in bug1 and bug2 are a
bit different.  Instead of starting with unbruised decimals a.b and
letting bruising arise naturally by addition and subtraction, I started
with already bruised small integers, with no particular model of what
caused the bruising.  Bruising can happen in various ways and at
various rates and magnitudes.  To understand this aspect of bruising
one would need to explore a lot of scenarios that might lead to
bruising, not just the one that PC Week focused on in their December 16
article.

It seemed to me that the most useful information would be obtained by
directly studying the impact of bruising, *independently of* its cause,
on error rates and magnitudes, as a function of the magnitude of the
bruising.  One could then extrapolate from this raw data to any
particular scenario involve bruising at a given rate and level.  My
experiments yielded the following basic properties of bruised
integers.

1.  The level of bruising that irritated the bug the most is around
10^-6.  Higher than 10^-4 and the bug no longer recognized it as
bruising since it was interfering with the requisite pattern of 4
special bits followed by 8 1's.

2.  For integers in the range 1 to 1000, with 10^-6 bruising, an error
greater than 10^-5 happens every 70,000 divisions, while one greater
than 10^-7 happens every 2,500 divisions.

3.  Reducing the limit from 1000 to 100 reduces the above 1/70,000 rate
to 1/2,000 and the above 1/2,500 rate to 1/200.

I agree this is a lot higher than anything PC Week found.  I also agree
with those posters who have questioned PC Week's interpretation of
their own results as placing them *between* IBM and Intel.  If anything
it makes PC Week more extreme than IBM (but not as extreme as the above
data on pure sources of small bruised integers).

It is natural to ask whether small bruised integers can arise in
practice and in what quantities and at what levels of brusing.  One way
that they can arise naturally is from any data source that does its own
decimal truncation.  Such a source might well produce 10^-6 bruising at
a very high rate.  And one can come up with other scenarios for
bruising at these levels.  One such is the Pentium itself, whose errors
are at just the right level to really arouse the bug: the Pentium will
get much more angry with its own 10^-5 to 10^-7 errors than those
arising via normal truncation on any machine (superlight bruising) at
around 10^-18.

But in view of the enormous variability of both applications and data
encountered by those applications, I don't see that a terribly useful
purpose can be served by speculating on what *might* happen.  Far
better for each user to examine their own application to determine
whether bruising is likely to constitute a serious problem for them.
Until a user has determined such statistics for the typical ranges of
data encountered in one's own application (as opposed to what Intel
says you encounter), that user cannot rule out with certainty error
rates and magnitudes as high as those indicated in item 3 above.

Another point to bear in mind is that there may lurk yet higher rates
via some other mechanism than small bruised integers.  Users need to be
on the lookout for such situations.

So yes, PC Week may have understated the seriousness of the problem.
But I think even the picture they have painted is serious enough that
users should be very concerned as a result of the PC Week article.

PC Week's main purpose seems to be the same as mine: to send a warning
signal alerting unsuspecting users to pay close attention to their
applications.  This should include learning more about the bug than PC
Week has to offer, and hopefully people will install signposts to
indicate where to find such additional information.  The IBM report is
one such place, mathworks.com's ftp/www site is another, my /pub/FDIV
directory on Boole.Stanford.EDU is yet another, and hopefully other
helpful information on the bug will come to light as more people join
in its investigation and more is learned about it.

There is a lot more to this business than pure technology, a point Intel
made in its December 20 repentium.
-- 
Vaughan Pratt			      FTP:  boole.stanford.edu:/pub/FDIV/README
4.999999/14.999999 has 6 3's, not 4   http://boole.stanford.edu/boole.html
				What you see when you add isn't what you've got
				Four quarters make a dollar, ten dimes do not

    I hear that there may be problems with getting incorrect Pentium heat
    sinks on replacement chips in various systems.  Does the Pentium chip
    come with a standard heat sink or does each system vendor provide
    one that suits that particular system package?
    
    Mark
    

+-+-+-+-+-+-+-+                                                 -----------  

|d|i|g|i|t|a|l|                   09-Jan-95                      LIVE WIRE

+-+-+-+-+-+-+-+                  INDUSTRY NEWS                  -----------


    INTEL'S NEW PENTIUM CHIP REQUIRES PROPER COOLING UNIT

                                                                      

    Following adverse publicity suffered by Intel after it was revealed

    that its Pentium chip contained a fault there has been a warning that

    the replacement chips must be installed with the correct cooling

    devices, or sinks, if overheating problems are not to be created.

    Manufacturers such as Dell have accepted that there may be an element

    of confusion regarding which heat sinks to fit to the new chips.


    Wall Street Journal, Europe. 9th January 1995

>    sinks on replacement chips in various systems.  Does the Pentium chip
>    come with a standard heat sink or does each system vendor provide
>    one that suits that particular system package?

The latter.

(I've got a Dell system, I'm waiting for Dell to send me a chip+heatsink
 combo...)