From: "James Giles" <jamesgiles@worldnet.att.net>
Subject: Re: Fortran or Ada?
Date: 1998/10/06
Date: 1998-10-06T00:00:00+00:00 [thread overview]
Message-ID: <6veadj$rqj@bgtnsc02.worldnet.att.net> (raw)
In-Reply-To: 361A98CB.444AD094@lmco.com
Mark A Biggar wrote in message <361A98CB.444AD094@lmco.com>...
>James Giles wrote:>> There are 2^128 different possible divide operations (each operand
>> having 2^64 different possible values) - and that's assuming that you
>> don't have to test each pair of operands for each possible value of
>> the exponent and sign (in which case there are nearly 2^160 different
>> operand pairs - each operand having 2^80 different values). Now,
>> assuming that a Pentium class machine can test 100 million operations
>> per second (an overestimate to say the least), it would take over 10^30
>> seconds to test all 2^128 divides. This still assumes you have an
>> independent source of the correct answer for each divide to test
>> against! Running, say, 1000 machines in parallel, each testing different
>> divides, would reduce the time needed to "just" 10^27 seconds. A
>> year has on the order of 3*10^7 seconds.
>
>You don't actuall actually have to test all 2^128 cases to be "exhaustive".
>First off you can factor the handling of exponents from that of mantissa's.
Yes, I assumed that (as I explicitly pointed out). If you couldn't separate
the significands from the exponent parts the number would be 2^158 cases
(minus a few - since there are NAN's that needn't be tested). If, further,
you couldn't separate out the sign bit, you'd have 2^160 cases. Remember,
the Intel chip uses extended-double internally - each operand is 80-bits
wide.
>In addition, the pentium algorithm is a base 4 division method, it works
>two bits at a time and uses some ROM table look-ups for partial results.
>The errors were in those tables, not the algorithm. A set of test cases that
>ran through all possible exponents combinations, and a sufficient set
>of mantissa's such that every table entry was use at least once would have
>found the pentium bug. Someone later said that such a test set could
>have been run in less than 10 minutes.
Yes, it's always possible, *after* you've found the bug, to think of a test
which would have detected it in short order. I was addressing the claim that
a genuinely exhaustive test was possible. It clearly wasn't.
--
J. Giles
next prev parent reply other threads:[~1998-10-06 0:00 UTC|newest]
Thread overview: 96+ messages / expand[flat|nested] mbox.gz Atom feed top
[not found] <36068E73.F0398C54@meca.polymtl.ca>
1998-09-22 0:00 ` Fortran or Ada? Gisle S{lensminde
1998-09-22 0:00 ` Jeff Templon
1998-09-22 0:00 ` dewarr
1998-09-23 0:00 ` Jeff Templon
1998-09-23 0:00 ` Corey Minyard
1998-09-24 0:00 ` Craig Burley
1998-09-25 0:00 ` dewarr
1998-09-25 0:00 ` Jonathan Guthrie
1998-09-26 0:00 ` Craig Burley
1998-09-26 0:00 ` dewarr
1998-09-26 0:00 ` Craig Burley
1998-09-26 0:00 ` Robert B. Love
1998-09-24 0:00 ` Joel Seidman
1998-09-24 0:00 ` Marc A. Criley
1998-09-24 0:00 ` Jeff Templon
1998-09-25 0:00 ` Dale Stanbrough
1998-09-30 0:00 ` Daniel Barker
1998-09-30 0:00 ` Lawrence Kirby
1998-10-01 0:00 ` Aaron Crane
1998-10-02 0:00 ` Fortran or Ada or gobbledygook? Wes Groleau
1998-10-05 0:00 ` Fortran or Ada? Terry Devine
1998-09-25 0:00 ` dewarr
1998-09-24 0:00 ` dewarr
1998-09-24 0:00 ` Robert I. Eachus
1998-09-24 0:00 ` William Clodius
1998-09-25 0:00 ` dewarr
1998-09-25 0:00 ` dewarr
1998-09-25 0:00 ` Robert I. Eachus
1998-09-25 0:00 ` dewarr
1998-09-25 0:00 ` jbs
1998-09-26 0:00 ` dewarr
1998-09-28 0:00 ` jbs
1998-09-29 0:00 ` Gautier.DeMontmollin
1998-09-29 0:00 ` Dean F. Sutherland
1998-09-29 0:00 ` Dean F. Sutherland
1998-09-29 0:00 ` Dean F. Sutherland
1998-09-29 0:00 ` William B. Clodius
1998-09-30 0:00 ` jbs
1998-09-30 0:00 ` dewarr
1998-09-30 0:00 ` jbs
1998-09-30 0:00 ` William Clodius
1998-09-30 0:00 ` William Clodius
1998-10-03 0:00 ` Niklas Holsti
1998-10-03 0:00 ` Toon Moene
1998-10-03 0:00 ` Niklas Holsti
1998-10-03 0:00 ` Toon Moene
1998-10-04 0:00 ` Niklas Holsti
1998-10-05 0:00 ` Michel OLAGNON
1998-10-05 0:00 ` Ian St. John
1998-10-05 0:00 ` dewarr
1998-10-05 0:00 ` Ian St. John
1998-10-06 0:00 ` dewarr
1998-10-06 0:00 ` Ian St. John
1998-10-08 0:00 ` Offtopic Airport Diversion (Was: Fortran or Ada?) Harold Stevens ** PLEASE SEE SIG **
1998-10-08 0:00 ` Ian St. John
1998-10-08 0:00 ` Fortran or Ada? Gary L. Scott
1998-10-06 0:00 ` Toon Moene
1998-10-06 0:00 ` Jonathan Guthrie
1998-10-06 0:00 ` James Giles
1998-10-06 0:00 ` Mark A Biggar
1998-10-06 0:00 ` James Giles [this message]
1998-10-07 0:00 ` dewarr
1998-10-07 0:00 ` dewarr
1998-10-05 0:00 ` Richard D Riehle
1998-10-05 0:00 ` dewarr
1998-10-06 0:00 ` Michel OLAGNON
1998-10-07 0:00 ` Ian St. John
1998-10-02 0:00 ` Robert I. Eachus
1998-10-02 0:00 ` jbs
1998-10-02 0:00 ` William Clodius
1998-10-03 0:00 ` jbs
1998-10-03 0:00 ` Larry Elmore
1998-10-06 0:00 ` Robert I. Eachus
1998-10-06 0:00 ` Pat Rogers
1998-10-02 0:00 ` Geoff Bull
[not found] ` <6udre0$ha1$1@nnrp1.dejane <6utg60$h6l$1@nnrp1.dejanews.com>
1998-10-01 0:00 ` robin_v
1998-09-22 0:00 ` Larry Kilgallen
1998-09-22 0:00 ` Corey Minyard
1998-09-22 0:00 ` Rakesh Malhotra
1998-09-23 0:00 ` Frank Ecke
1998-09-23 0:00 ` bglbv
1998-09-23 0:00 ` Robert I. Eachus
1998-09-24 0:00 ` Richard D Riehle
1998-09-23 0:00 Marin David Condic, 561.796.8997, M/S 731-96
-- strict thread matches above, loose matches on Subject: below --
1998-09-23 0:00 Marin David Condic, 561.796.8997, M/S 731-96
1998-09-23 0:00 ` Gisle S{lensminde
1998-09-24 0:00 ` John McCabe
1998-09-24 0:00 ` Dean F. Sutherland
1998-09-24 0:00 ` Gisle S{lensminde
1998-09-24 0:00 ` Samuel T. Harris
1998-09-24 0:00 Walt Brainerd
1998-09-25 0:00 ` dewarr
1998-09-25 0:00 ` Robert I. Eachus
1998-10-05 0:00 Condic, Marin D.
1998-10-05 0:00 robin
1998-10-05 0:00 Robert I. Eachus
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