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From: pbickers@tamaluit.phys.uidaho.edu (Paul Bickerstaff)
Newsgroups: comp.benchmarks
Subject: harmonic series (was Re: more bc babble)
Message-ID: <1990Dec15.094523.10622@groucho>
Date: 15 Dec 90 09:45:23 GMT
References: <OLES.90Dec13213301@kelvin.uio.no> <1990Dec11.163826.5439@eagle.lerc.nasa.gov>
Sender: @groucho
Reply-To: pbickers@tamaluit.phys.uidaho.edu (Paul Bickerstaff)
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Lines: 77

> 
> Another easy-to-memorize benchmark is the computation of the sum
> of the first 10 million terms in the harmonic series.

I've also used this as quick but (very rough) guide to floating point
speed (but mainly to
orient myself on a new system ).
> This is a FORTRAN version, it should not be too hard to translate
> even without f2c :-)
> 
>       PROGRAM RR
>       DOUBLE PRECISION R
>       R=0.0
>         DO 10 I=1,10000000
                            ^^^^^^^^
As a general tutorial type comment, one should always sum series  by
doing the smallest terms
first. This is for numerical accuracy. OK, the smallest here is 10^-7
and we're using double
precision but the comment still stands as a matter of programming
practice and summing
in the reverse order may give very different results.
>         R=R+1/DBLE(I)
> 10      CONTINUE
>       WRITE(*,*)R,I
>       END
> 
> This one is obviously testing floating-point perfomance only. The

Idon't think this is true. It is also testing a tight do loop.
> emphasis on divisions might give biased results. It vectorizes
                                           ^^^^
This and other things *will* give biased results. Heck, *every*
benchmark gives biased results.
The trick is to choose a benchmark (or create your own) which matches
your applications.  There
is not a single benchmark, MFLOPS, MIPS, SPECMARKS or whatever that
means anything
worthwhile if you don't know exactly how relevant it is to what you're doing.

If the harmonic series has any value at all it is in educating people
just how useless benchmarks
are. eg. (I won't include exact code, but mine was double precision with
reverse order of summation)

(also, I only summed 1 million terms)

IBM   RS6000/320    2.14   xlf
                                    1.41   xlf -O
                                    1.33   xlf -O -Q'OPT(3)'            
      (July '90 results)

Mips Magnum 3000  1.2     f77 -O0   (ie no optimizations)
                                     0.9     f77   (default level = f77 -O1)
                                     0.5     f77 -O2                    
                 (Fortran 2.11 , RISCos 4.51)

Times are all user times in secs.

So how come a 3.6 MFLOP machine can run Fortran at about twice the speed
of a 7.4 MFLOP
machine? (Yes I have this the right way around!)

Answer: Easy.

(This article is not intended as IBM bashing. I  have Fortran codes
which do run  much faster
on the RS6000.  The IBM does excell at the LINPACK benchmark but unless
you do a lot of 
100x100 array manipulations the 7.4 MFLOP LINPACK  number clearly does
n't mean much.
Nor do the times for the harmonic series. )
  

Paul Bickerstaff                 Internet: pbickers@tamaluit.phys.uidaho.edu
Physics Dept., Univ. of Idaho    Phone:    (208) 885 6809
Moscow ID 83843, USA             FAX:      (208) 885 6173