Re: Fortran or Ada?

[dewarr@my-dejanews.com]

In article <6veadj$rqj@bgtnsc02.worldnet.att.net>,
  "James Giles" <jamesgiles@worldnet.att.net> wrote:
>
> 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.


Reread my original post, no one ever claimed that a genuinely exhaustive
test was possible in this case. I said it was "almost possible", by which
I meant precisely that the critical component, namely the table lookup
part of the algorithm, could indeed have been tested exhuastively, and
should have been, no hindsight required!

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