Autor: Jerzy Pastusiak (pastupam_at_uoo.univ.szczecin.pl)
Data: Fri 18 Nov 1994 - 18:48:43 MET
Przepraszam, ze troche poza tematem, ale moze to byc wazne dla nas
wszystkich komputerowcow, w taki lub inny sposob. Informacja dotyczy
bledu w Pentium, druga czesc jest odpowiedzia pracownika Intela. Kolejne
listy potwierdzaja niestety informacje. Dyskusja toczy sie na SAS-L,
liscie dyskusyjnej programu statystycznego SAS.
Przesylam przdrowienia, J.P.
> From: SMTP%"njage_at_moeulx.morgan.edu" 16-NOV-1994 17:52:52.32
> To: JAMES
> CC:
> Subj: pentium chip has serious flaw...
>
> Date: Wed, 16 Nov 1994 19:42:56 -0500
> From: njage_at_moeulx.morgan.edu (E. Njage)
> Message-Id: <9411170042.AA01867_at_moeulx.morgan.edu>
> To: kci-net_at_media.mit.edu
> Subject: pentium chip has serious flaw...
>
> Pentium Floating Point Division Bug
>
> There has been a flurry of activity the last fews days on the
> Internet news group, comp.sys.intel, that should interest MATLAB
> users. A serious design flaw has been discovered in the floating
> point unit on Intel's Pentium chip. Double precision divisions
> involving operands with certain bit patterns can produce incorrect
> results.
>
> The most dramatic example seen so far can be extracted from a
> posting last night by Tim Coe of Vitesse Semiconductor. In MATLAB,
> his example becomes
>
> x = 4195835
> y = 3145727
> z = x - (x/y)*y
>
> With exact computation, z would be zero. In fact, we get zero on
> most machines, including those using Intel 286, 386 and 486 chips.
> Even with roundoff error, z should not be much larger than eps*x,
> which is about 9.3e-10. But, on the Pentium,
>
> z = 256
>
> The relative error, z/x, is about 2^(-14) or 6.1e-5. The computed
> quotient, x/y, is accurate to only 14 bits.
>
> An article in last week's edition of Electronic Engineering Times
> credits Prof. Thomas Nicely, a mathematics professor at Lynchburg
> College in Virginia, with the first public announcement of the
> Pentium division bug. One of Nicely's examples involves
>
> p = 824633702441
>
> With exact computation
>
> q = 1 - (1/p)*p
>
> would be zero. With floating point computation, q should be on
> the order of eps. On most machines, we find that
>
> q = eps/2 = 2^(-53) ~= 1.11e-16
>
> But on the Pentium
>
> q = 2^(-28) ~= 3.72e-09
>
> This is roughly single precision accuracy and is typical of the
> most of the examples that had been posted before Coe's analysis.
>
> The bit patterns of the operands involved in these examples
> are very special. The denominator in Coe's example is
>
> y = 3*2^20 - 1
>
> Nicely's research involves a theorem about sums of reciprocals
> of prime numbers. His example involves a prime of the form
>
> p = 3*2^38 - 18391
>
> We're not sure yet how many operands cause the Pentium's floating
> point division to fail, or even what operands produce the largest
> relative error. It is certainly true that failures are very rare.
> But, as far as we are concerned, the real difficulty is having to
> worry about this at all. There are so many other things than can
> go wrong with computer hardware, and software, that, at least, we
> ought to be able to rely on the basic arithmetic.
>
> The bug is definitely in the Pentium chip. It occurs at all clock
> rates. The bug does not affect other arithmetic operations, or the
> built-in transcendental functions. Intel has recently made changes
> to the on-chip Program Logic Array that fix the bug and is now
> believed to be producing error free CPUs. It remains to be seen
> how long it will take for these to reach users.
>
> An unnamed Intel spokesman is quoted in the EE Times article as
> saying "If customers are concerned, they can call and we'll replace
> any of the parts that contain the bug." But, at the MathWorks,
> we have our own friends and contacts at Intel and we're unable
> to confirm this policy. We'll let you know when we hear anything
> more definite. In the meantime, the phone number for Customer
> Service at Intel is 800-628-8686.
>
> -- Cleve Moler
> Chairman and Chief Scientist
> The MathWorks, Inc.
> moler_at_mathworks.com
>
> ------------------------------------------------------------------------
> Sender: "SAS(r) Discussion" <SAS-L%AWIIMC12.bitnet_at_plearn.edu.pl>
> From: Thomas M Skinner <Thomas_M_Skinner%CCM.FM.INTEL.COM_at_plearn.edu.pl>
> Subject: Re[2]: Pentium Error Warning Test on SAS
> Comments: To: sas-l_at_uga.cc.uga.edu
> To: Multiple recipients of list SAS-L <SAS-L_at_AWIIMC12.BITNET>
>
> Folsom, California
> November 17, 1994
> Foggy, 50's
> Dear SAS-Lers,
>
> Andy Parks whose post you've probably already received, had contacted me
> yesterday about this and I forwarded it on to our Strategic Software Technology
> Manager for SAS Institute. At that time I was thinking it was a problem
> isolated to SAS. I did get a reply back with a little background info, which
> indicated that it was a very remote bug in the FPU, with a chance of 1 in 10
> million of occurring. It had been apparently discovered by a scientist doing
> Prime number research. It is a generic problem and in no way associated with
> SAS software.
>
> I'm certainly not trying to discount the problem, but I also don't think there's
> reason to panic. Certainly in the SAS community any stats that I could provide
> will be gazed upon with critical eyes as is native to folks of the statistical
> discipline. I've contacted the Pentium Compatibility labs (with whom I've had
> some dealings in the past, in terms of setting up SAS as a test application for
> performance teting of the FPU), and I'll pass on what I can when I get a reply.
>
> This is by no means a corporate statement and should not be taken that way. The
> best way to handle this situation is to contact the vendor of your machine and
> ask them if they intend to recall their products. Just as in the automotive
> business, you'll not go to the maker of the car seat which might be the cause
> for a recall, but to the car manufacturer. However, I'm sure the intel customer
> information 800 number folks would be happy to answer any reliability questions
> with regard to the chip.
>
> Intel-Insider,
> Tom Skinner
>
To archiwum zostało wygenerowane przez hypermail 2.1.7 : Wed 19 May 2004 - 15:47:07 MET DST