Path: utzoo!attcan!uunet!mcsun!hp4nl!charon!dik
From: dik@cwi.nl (Dik T. Winter)
Newsgroups: comp.arch
Subject: Re: RS6000 Multiply/Accumulate instruction
Keywords: RS6000, floating-point multiply, fp add
Message-ID: <8910@boring.cwi.nl>
Date: 21 Mar 90 21:15:35 GMT
References: <5827@udccvax1.acs.udel.EDU> <8907@boring.cwi.nl> <5900@udccvax1.acs.udel.EDU>
Sender: news@cwi.nl (The Daily Dross)
Organization: CWI, Amsterdam
Lines: 48

In article <5900@udccvax1.acs.udel.EDU> mccalpin@vax1.acs.udel.EDU (John D Mccalpin) writes:
 > I wrote about the RMS error in the solution of the LINPACK 1000x1000
 > system of equations on the new IBM RS/6000 vs various other machines.
 > 
 > The RMS error that I have been posting is based on the fact that the
 > matrix is chosen in such as way that the solution consists of 1000
 > identical elements equal to 1.0d0.  It does this by generating a 
 > pseudo-random matrix and then re-scaling by the row sums (I think this
 > is how it was done).
 > 
And shows me wrong when I assumed that the input data might be different.
Thanks for the info.

 > I have used the subroutine DGECO from LINPACK to estimate the condition
 > number of this matrix and it is about 200,000, as I recall.
 > 
This is interesting; it is not extremely high but not very low either.
(Singular values of an order of 1.0e-5 are very reasonable.)  On the
other hand, such a condition number indicates a certain sensitivity to
the way results are calculated.  So even if more precision is used
doing some calculations this might result in a less favourable end result.

 >                                           My experience has been that
 > even the direction of the error (i.e. better or worse answers) is
 > data-dependent.  
Very true.
 > 
 > I am still trying to get the machine to run with the multiply/add
 > function separated, but the new O/S that they put on the FSU machine
 > seems to be broken....
I look forward to the results.

A concluding remark.  In my opinion the use of linear system solvers to
detect accuracy of arithmetic on different machines is debatable at least.
All such comparisons depend on a forward analysis (I have got this result;
it should be so-and-so; this is the error).  For linear sytems this is
not very reliable.  To get an historical perspective:  in the forties and
early fifties it was thought that direct methods to solve linear systems
(i.e. LU) could not give good results.  The reason is that forward error
analysis fails on this problem.  It was J.H.Wilkinson who showed that such
methods could be used favorably (in 1956 or thereabouts) by the use of
backward error analysis (i.e. my result is the exact solution for a
system that is very close to the original problem).  So any comparison
of the true solution and the numerical solution should be viewed with
some restraint.
-- 
dik t. winter, cwi, amsterdam, nederland
dik@cwi.nl