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RE: IEEE754R11
All,
Could someone translate these material into specific suggestions for
changes to the current 754 draft, as could/should be submitted via
comments?
I have a hard time translating from these general discussions to
specific changes in the specification that might be viewed as valuable.
Cheers,
DVJ
-----Original Message-----
From: stds-754@xxxxxxxx [mailto:stds-754@xxxxxxxx]On Behalf Of David
Hough 754R work
Sent: Friday, July 06, 2007 4:01 PM
To: ae35@xxxxxxxxxxxxxxxxxxxx; boein@xxxxxxxxxx; stds-754@xxxxxxxx
Subject: Re: IEEE754R11
Concerning my simplest possible example of irreproducible results,
z = a + b + c
Prof. Kulisch wrote a few days ago:
I think that two diffenrent things are conflated in the discussion of
this simple example:
a) errors in the data that occur during a computation and
b) errors in the arithmetic.
a) is an unavoidable source of errors. Of course, the data are
frequently contaminated by
roundoff. But an error in the data does not justify error in the
arithmetic. The vendor is
responsible for the quality of the arithmetic. To be as accurate as
possible is essential.
Sloppy arithmetic prevents users from solving problems correctly when
the data are exact.
In scientific computation the data are seldom exact, so the problem is
to get the final uncertainty due to roundoff to be much less than the
final uncertainty due to the input data and due to the algorithm.
So getting exact or correctly-rounded results for large sums or
dot products
is usually not economic.
Realistic computations usually involve many such operations
whose rounded results are combined. The economic case for
even 128-bit
floating-point hardware is arguable.
Variable precision is indeed an answer for a certain small class
of users
operating on data they consider exact or very precise,
but 754R has repeatedly considered
and rejected standardizing variable precision in this revision.
The goal of a typical roundoff error analysis of an approximate
process on inexact inputs is not to prove that the result
is correct, but that roundoff has not made the result worse than it would
have been in exact arithmetic. Those analyses are difficult enough
that one would prefer not to repeat them for every optimization level of
every release of every compiler for every platform.
So the goal of the reproducibility proposals is to make it possible to
do one analysis that could be applied to each platform the
program is run upon.
"Possible" does not mean "always desirable" because there are very real
performance costs associated with constraining results to be
reproducible.