🚀 go-pugleaf

Responding to my earlier comments,
in article <9106120131.AA20868@ucbvax.Berkeley.EDU>, jbs@WATSON.IBM.COM writes:
> 
>> Various versions of the Linpack benchmark all have in common
>> that the data is taken from a uniform random distribution, producing problems
>> of very good condition.   So the worst possible linear
>> equation solver algorithm running on the dirtiest possible floating-point
>> hardware should be able to produce a reasonably small residual, even for
>> input problems of very large dimension.
> 
>          This is untrue.  Consider pivoting on the column element of
> smallest magnitude while using IEEE single precision.  I don't believe
> n has to be very large before you are in big trouble.

I should have said "the worst PROBABLE algorithm" - no pivoting at all rather
than agressively choosing the worst possible pivot.  It ought to be possible to
try this out by disabling the pivot selection in the Linpack benchmark.

>> This means that the same algorithms and input data
>> will fail on some computer systems and not on others.
> 
>          If you know of a single realistic application where the diff-
> erence between 64 bit IEEE rounded to nearest and 64 bit IEEE chopped
> to zero makes a significant difference in the maximum performance ob-
> tainable I would like to see it.

I doubt you'll find anything like this in normal scientific computation
- the difference in problem domain between floating-point systems with
identical exponent and significand fields and rounding schemes
comparable in cost and care is rarely likely to be extremely
noticable.  I would expect to notice the difference in problems like
orbit computations, however - rounding should yield acceptable results
for longer simulated times than chopping, even if everything else is
equal, simply because the statistics of rounding are more favorable.  I
have also heard that the details of rounding are important in financial
calculations of bond yields.

More to the point of benchmarking defined by vendor consortia, the
differences in applicable domain between 32-bit IBM 370 format and
32-bit IEEE, or between 64-bit Cray format and 64-bit IEEE, or even
between HP and TI hand calculators with 10 displayed digits, has been a
part of the experience of a number of comp.arch readers.   In the two
former cases you can often get by with twice as much of the dirtier
precision.  In the Cray case that's much slower, however, and may
eliminate most of the supercomputer's advantage over a workstation.
The IBM 370 case may be slower too if the problem involves much more
than +-*.
-- 

David Hough

dgh@validgh.com		uunet!validgh!dgh	na.hough@na-net.ornl.gov