pmontgom@oak.math.ucla.edu (01/18/90)
Several individuals submitted times for the benchmark I posted
ten days ago during the controversy about integer multiplication and the
SPARC. Here is a summary of the responses. It seems the marketplace
has more VAXes than I realized; I list them first. Nobody
reported trying a different version of the MODMUL statement function.
For reference purposes, the SUN 3/280 had a geometric mean time
of 1.25 sec. My SPARC time (don't know which model) was 1.00 sec.
The Alliant FX/80 single-processor time was 1.02 sec (unvectorized)
and 0.54 sec vectorized. The reported times for the SUN 4/190 (0.48 sec),
MIPS RC3240 (0.36 sec), and Hitachi AS/9180 (0.24 sec) are the best yet.
---------- From: (Stephen Tihor) <TIHOR@ACF1.NYU.EDU>
OK. FYI: VMS 5.1. FORTRAN v5, noopt [machine not specified]
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
0.63 1.59 1.17 2.12 1.14 1.30 10.61 0.85 2.39 1.29 1.89 1.61 sec
opt
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
0.53 0.84 0.46 1.41 0.48 0.68 8.57 0.57 2.21 1.16 1.14 1.03 sec
The numbers should improve with the new compiler (FORTRAN-HPO I believe its
called.)
VAX-63n0
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
0.77 1.58 1.18 2.40 1.13 1.38 9.11 0.73 2.06 1.11 2.10 1.60 sec
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
0.65 0.86 0.49 1.79 0.43 0.60 6.89 0.46 1.91 0.98 1.10 0.98 sec
VAX-8650
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
0.46 1.02 0.80 1.41 0.78 0.92 7.33 0.57 1.57 0.89 1.29 1.10 sec
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
0.33 0.56 0.32 0.95 0.33 0.48 5.88 0.39 1.54 0.77 0.75 0.69 sec
VAX-8600
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
0.62 1.57 1.15 2.12 1.13 1.33 10.58 0.85 2.33 1.26 1.85 1.60 sec
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
0.54 0.85 0.45 1.41 0.47 0.67 8.47 0.55 2.21 1.16 1.13 1.02 sec
---------- From: jim@wucs1.wustl.edu (James William Studt)
I've run your benchmark on a selection of 'modern' vaxes.
This is under VMS 5.3, VAX Fortran 5.1.
On an 8530 with 32M of memory
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
0.56 0.78 0.67 2.04 0.66 0.77 7.66 0.47 2.01 1.19 1.65 1.14 sec
On a VS3100 with 32M of memory
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
1.00 1.28 0.73 2.60 0.62 0.83 10.29 0.66 2.86 1.52 1.65 1.45 sec
On a VS3520 with 16M of memory
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
0.94 1.18 0.68 2.46 0.60 0.78 9.25 0.60 2.58 1.34 1.45 1.34 sec
On a vs2000 with 6M of memory
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
2.90 4.09 3.01 10.08 2.72 3.25 24.94 2.35 7.77 4.30 5.51 4.84 sec
---------- From: Chris Siebenmann <cks@white.toronto.edu>
DECstation 3100, 24M ram:
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
0.22 0.42 0.37 0.73 0.55 0.65 4.26 0.21 0.98 1.38 0.70 0.64 sec
VaxServer 3800, 32M ram:
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
0.78 1.68 0.82 3.90 0.73 0.93 5.27 0.48 1.87 1.40 1.68 1.37 sec
---------- From: John Hascall <JOHN@FOREST.ECIL.IASTATE.EDU>
VAXstation 3200, 8Mb, VMS5.2, Fortran/Optimize/NoCheck/NoDebug
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
0.89 1.13 0.70 2.32 0.55 0.72 8.99 0.59 2.52 1.37 1.42 1.29 sec
Note that the times are in REAL seconds not CPU seconds (since I already
had a routine to return those), but the correlation seems very high anyway.
Hitachi Data Systems AS/9180, 64Mb, MVS/XA, VSFORTRAN V2/OPT=3
GENER DBLE SNGL CMPLX INTGR MODLR TRLDIV PRBPRM GCD BINDEC CFRAC GEO MEAN
0.05 0.10 0.09 0.32 0.11 0.17 2.39 0.16 0.60 0.52 0.45 0.24 SEC
Note I only used 1 of the 2 CPUs and did not use the vector processor as
I haven't clue how to do either.
---------- From: alan@ernest.csc.ti.com (Alan Edmonds)
Enclosed are the timing results for a NS 32032 at 10 MHz. I have
an Opus 100PM Unix co-processor board installed in a TI Business-Pro
(AT compatible) with an 80286 at 6 MHz.
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
7.20 14.83 13.45 42.95 4.18 10.78 38.10 3.83 10.00 13.23 14.78 12.07 sec
---------- From: mark@mips.COM (Mark G. Johnson)
MIPS RC3240 compiled with f77 -O (upgrade of earlier M/120 machine)
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
0.08 0.26 0.23 0.34 0.39 0.46 2.84 0.10 0.63 0.60 0.46 0.36 sec
{This falls between the single-processor Alliant with vectorization and
optimization, and the 6-processor Alliant with V&O, in Geo mean performance.}
For those who desire to bicker about the benchmark's representative-ness
of "real code", or potential lack thereof, here is a teeny bit of profiling
data. A single line of source, marked below with >>>>, is responsible for
over 1/4 of all cycles consumed by the program (dynamically, on RC3240):
do 100 j = 5, NINT(SQRT(REAL(n))), 6 [575]
>>>> if (MOD(n,j).eq.0 .or. MOD(n,j+2).eq.0) then [576]
PRIME = .FALSE. [577]
return [578]
end if [579]
100 continue [580]
---------- From: khb@Sun.COM (Keith Bierman - SPD Advanced Languages)
f77v1.3 (not released yet) -fast -O4 -Bstatic
SUN 4/330
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
0.18 0.20 0.17 0.85 0.76 0.61 12.43 0.30 0.82 1.11 0.71 0.63 sec
SUN 4/490
Gener Dble Sngl Cmplx Intgr Modlr TrlDiv PrbPrm GCD BinDec Cfrac Geo mean
0.14 0.17 0.11 0.64 0.60 0.46 9.64 0.26 0.55 0.82 0.56 0.48 sec
Keith Bierman also says the reason the Cmplx/Sngl ratio
is higher on the SUNs than other machines is that SUN does the
complex multiply in double precision rather than single precision,
to emphasize precision over speed.
Curiously, just as his response arrived, I say an article
in C.B. Dunham in the October, 1989 SIGNUM Newsletter
recommending the use of double precision arithmetic in complex
multiplication and division.
----------
From: barnett@unclejack.crd.ge.com (Bruce Barnett)
>In article <2131@sunset.MATH.UCLA.EDU> you write:
>|
>| The SUN 3s have OS version 4.2.
>Sun never has a OS version called 4.2. There were based on dsb4.2, but
>all of them are.
My mistake - the SUN 3 times were for OS version 3.5.2.
--------
Peter Montgomery
pmontgom@MATH.UCLA.EDU
Department of Mathematics, UCLA, Los Angeles, CA 90024