Subject: Summary:Benchmarks

From: Carles Colominas <[email-masked]>
Date: Tue, 22 Oct 1996 11:26:49 +0100 (GDT)

Dear Netters,

 Some days ago I posted a message about new HP and SGI workstations perfomance.
My original question and answers are shown below.

The last part of this message is a review by Martyn F. Guest at CCLRC Daresbury
Laboratory about 'Performance of Various Computers in Computational Chemistry' 
that includes lots of useful data.

Thanks to all who answered:
	Steen Hammerum
	Bill DeSimone
	Jose Luis Garcia de Paz
	Oakley H. Crawford
	Marc C. Nicklaus
	Vikram Varma
	Alexander Hofmann
	Martyn F. Guest

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From: Steen Hammerum <[email-masked]>

I recently asked the very same question, and here is the summary I posted:

------------------------------------------------------------------------

Summary: Speed of new HP and SGI workstations

I recently asked this group for advice with regard to the performance
of new HP and SGI workstations running the Gaussian programs

------------------------------------------------------------------------

Does anyone have or know of benchmarks for Gaussian 94 or related programs
running on the new SGI and HP chips (R10000 and PA8000), or other
information to assist us before we decide on new machinery?

We are currently considering SGI Power Indigo 2 and HP C160 workstations
that will be used predominantly for Gaussian calculations, but we are not
sure how well the SPECint95 and SPECfp95 numbers allow us to assess the
relative performance.

-------------------------------------------------------------------------

---

Roberto Gomperts ([email-masked]) provided the following
comparison of the SGI R8000 and R10000 chips when running test178
>from the Gaussian 94 test suite (a single point, direct scf calculation
with 300 basis functions), using Gaussian 94, rev. D3.

   Machine	  Chip/Frequency	Sec. Cache	Time(min.)
Power Indigo2	   r8k/75 MHz		  2 MB		  8.04
Power Challenge	   r8k/90 MHz		  4 MB		  6.50
Power Indigo2     r10k/195 MHz		  1 MB		  7.30
Power Challenge	  r10k/195 MHz	          1 MB		  7.08
Power Challenge	  r10k/195 MHz		  2 MB		  5.95

The Power Challenge runs are done on 1 processor.  These are all CPU times. 
The Wall clock times are very similar to these (less than 20 sec. difference)

---

John Brodholt ([email-masked]) pointed me to

http://gserv1.dl.ac.uk/TCSC/disco/TechPapers/bench/bench.html

This site provides a detailed, critical and very useful
comparison of the performance of a wide variety
of newer workstations; unfortunately, no results obtained with HP PA8000
machines are included (html version not yet available, but a postscript
version can be downloaded).
The comparison is based on timing data obtained with GAMESS-UK 
(rather than Gaussian).  The results illustrate that the relative
performance varies quite a bit with the type of calculation undertaken.

---

Eric Billings ([email-masked]) pointed me to

http://www.ki.si/parallel/summary.html

The information was designed to compare parallel architectures, but the 
single CPU column provides useful information.

---

Finally, Glenn McEnroe ([email-masked]) suggested that I looked elsewhere:

"Regarding your question about SGI vs HP you should check out the latest
issue of Journal of Computational Chem V17 No. 11 1385-86 entitled
Viability of Molecular Modeling with Pentium based PCs. This article does
not compare these new chips for SGI and HP but it appears that you may be
better off running your application on a pentium based machine if Gaussian
94 is available for this platform."

---

Many thanks to everyone who answered.

----------------------------------------------------------------

Since writing the summary, I have had the opportunity to perform trisl
calculations on both new SGI and new HP machines.  The results with R10k
SGI machines confirm Roberto Gomperts' results (see summary), that is, the
new chip is very fast but not much faster than the old chip, and cache size
matters a lot.  My HP results have been somewhat disappointing, insofar as
the new chip in real life situations (if G94 calculations can be called
"real life") does not seem to be quite as fast as the benchmarks would lead
you to expect. 

Hope this helps,

Steen
-- 
	
Steen Hammerum                                           [email-masked]
Department of Chemistry                              (+45) 35 32 02 08
University of Copenhagen, Denmark               fax: (+45) 35 32 02 12

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From: [email-masked]

Carles,

	The AlphaStation 500 with the 500 MHz chip should perform at least 
	as well if not better than HP and SGI on Gaussian and AMBER.  A 
	customer in Isreal just bought an AlphaStation 500 to run Gaussian.
	I can see if this customer would talk to you if you are interested.

	Unfortunately all my Gaussian benchmarks are on AlphaServers , 
	which BTW, beat the competition on Gaussian benchmarks.
	Also, the UCSF data on AMBER is on very old AlphaStations.

		Bill DeSimone
		Science & Research Applications
		High Performance Computing
		DEC

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From: [email-masked]

Carles,

En la Univ Autonoma de Madrid se acaba de comprar un DEC de 8 cpu, en
competencia con un SGI de ocho r10000. Hicimos pruebas con el
gaussian (en eso estuve yo) y EN TODAS nos salio un 20% mas
repido el chip dec que el chip silicon.
 Hubo test del gaussian usando una sola cpu, usando varias (paralelo), etc.
No hubo color. La version gaussian para dec iba mejor que la gaussian
que habian modificado para silicon.
 Yo estuve en la comision tecnica como quimico cuantico y no tuve dudas.

  Un saludo

  Jose Luis Garcia de Paz

 quimica fisica aplicada
 3974263-4957

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From:[email-masked]

If you have access to the www, look at
http://www.netlib.org/performance/html/PDStop.html
for performance data on a vast array of machines.

Otherwise, send the following message to [email-masked], to receive
performance data in postscript files:

send performance.ps from benchmark
send mp-computers.ps from benchmark

Finally, if you want more info about netlib's collection, send the following
message:

send index

Good luck,
Oakley Crawford
----------------------------------------------------------------------------
Oakley H. Crawford                Phone:  +1-423-574-5048
Oak Ridge National Laboratory     Fax:  +1-423-574-6210
P. O. Box 2008, MS 6123           E-mail:  [email-masked]
Oak Ridge, Tennessee 37831-6123   Express delivery, add:  Bethel Valley Road 
USA
----------------------------------------------------------------------------

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From: "M. Nicklaus" <[email-masked]>

Dear Dr. Colominas,

We have a four-processor Digital AlphaServer 4/275 which we use mostly
to run Gaussian 94 and the Molecular Mechanics program CHARMM.  We are
very happy with it.  We have not done benchmark comparisons with an SG
R10000 system ourselves (since we don't have one), but I remember having
seen quite a few postings of, or at least pointers to, benchmarks with
ab initio and MM programs that included SGI, HP, and/or DEC systems, and
which should be retrievable from the CCL archives.  Hope this helps.

Regards,

Marc C. Nicklaus

------------------------------------------------------------------------
 Marc C. Nicklaus                        Lab. of Medicinal Chemistry
 e-mail: [email-masked]               National Cancer Institute, NIH
 Phone:  (301) 402-3111                  Bldg 37, Rm 5B29
 Fax:    (301) 496-5839                  BETHESDA, MD 20892-4255    USA
         WWW:  http://www.nci.nih.gov/intra/lmch/MCNBIO.HTM
------------------------------------------------------------------------

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From: Vikram Varma <[email-masked]>

Also consider the Pentium Pros - in parallel, you can get
a lot of bang for your buck!!
Vikram Varma
National Research Council of Canada        Phone: 613 993 5150
Institute for Biological Sciences          FAX:   613 952 9092
Room 3071 100 Sussex Drive,		   e-mail: [email-masked]
Ottawa, Ontario K1A 0R6			   www: http://nrcbsa.bio.nrc.ca/~varma
<<<<<

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From: Alexander Hofmann <[email-masked]>

Some Gaussian-benchmarks

http://www.chem.joensuu.fi/people/juha_muilu/Misc/benchmarks.html

regards

alex

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From: "M.F.Guest" <[email-masked]>

Dear Carles,

In response to your mailing, I thought you might find the attached of
value. This is a plain text version of an assessment of a wide variety
of machines in computational chemistry, including the R10000 and a
prototype version of the new HP machine. While it doesnt specifically
include GAUSSIAN and AMBER, I hope that you will find it of use.

Let me know if I can be of any further assistance.

Best regards

Martyn

******************************************************************
* Martyn F. Guest                                                *
* Head, Advanced Research Computing   email:  [email-masked] *
* CCLRC Daresbury Laboratory          FAX  :  +44 (0)1925 603634 *
* Warrington                          voice:  +44 (0)1925 603247 * 
* Cheshire WA4 4AD                                               *
* England, UK                                                    *
******************************************************************

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Performance of Various Computers in Computational Chemistry

Martyn F. Guest

September 1996

Abstract

This report compares the performance of a number of different computer
systems using a variety of software from the discipline of
computational chemistry. The software includes matrix operations, a
variety of chemistry kernels from quantum chemistry and molecular
dynamics, and a set of twelve quantum chemistry calculations using the
GAMESS-UK electronic structure program.

The comparison involves approximately fifty computers, ranging from a
Cray YMP-C98 to scientific workstations from IBM, Sun, Hewlett Packard,
Digital and Silicon Graphics, and Pentium Pro-based PCs.

1. Introduction

This report presents a performance evaluation through benchmarking of
a number of different computer systems specifically in the area of
computational chemistry.  This work has been ongoing since 1988, when
the intention was to include representative hardware typifying
supercomputers, superminis, workstations and the emerging class of
parallel, novel architecture machines.  Throughout the 1980's the cost
effective debate in scientific computing centred on the relative merits
of conventional vector supercomputers [1] and so-called superminis,
machines costing some 10% of supercomputers, and exhibiting some 10% of
supercomputer performance [2].  Over the past 7 years the supermini
category of computational resource has to a large extent disappeared
>from both the vocabulary and offerings of most hardware vendors, to be
replaced by high-end workstation servers. We have retained those
machines that originally belonged in the supermini bracket, the Convex
220, the FPS M64/60 [2] and Alliant FX2808, primarily to provide a
historical perspective at the evolution of workstation capabilities,
and how machines that typically fell in the $500K price range are now
outperformed by machines costing some 10% of this figure.

Supercomputers used in this report include the Cray X-MP, Y-MP, YMP/J90
and YMP/C98, and the Convex C3860.  A large number of workstations have
been benchmarked, including those from

 -  IBM, with the Power and Power2 Risc system RS6000-based models,
 -  Hewlett Packard with the HP/Apollo DN10020 and the PA-RISC based HP
model 9000 series, including the more recent PA8000 CPU. Note that the
latter was housed in a single-processor HP PA/9000-K460, with a 160 Mhz
PA8000 (and not 180 MHz).
 -  DEC, with the DEC Station 500, the AXP EV4-based 3000 series. and
the EV5-based 600, 800 and 2100 alpha series,
 -  Silicon Graphics, with the R3000-, R4000-, and R8000-based machines
including the Challenge, Power Challenge, Indy, Indigo and Indigo2,
Crimson, and 4D series, plus machines with the more recent R10000 and
R5000 CPUs.
 -  Stardent (1520, 3020 and VISTRA 800), and
 -  Sun 4/370, SPARCstation-2, SPARC-5 and SPARC-10 and the more recent
Hyper- and Ultra-SPARC processors (Ultra-1/140 and 170, and the
Ultra-2/200).

While workstations have, for the majority of scientific applications,
demonstrated their cost-effectiveness against vector supercomputers,
recent developments with PCs suggest that the position of the
workstation as the desktop system of choice is now under threat.  We
thus include for the first time one of the most recent offerings from
the PC marketplace, the 200 MHz Pentium Pro.

Parallel, or ``novel architecture'' machines include the iPSC/860 from
Intel, both transputer and i860-based Meiko Computing Surfaces, the
KSR-2 from Kendall Square Research, the Cray T3D and IBM SP2.

Machines featuring in this exercise, together with associated
configurations, are given in the Appendix.  We should stress from the
outset that our access to much of the hardware evaluated herein has
been at best short lived, and has often involved the temporary loan or
donation of machines as part of one of the hardware evaluation
exercises run at the Daresbury Laboratory. In many cases these machines
were not optimally configured in terms of either memory, or high speed
disk, and consideration of the results presented here should be viewed
in that light.

Following an introductory evaluation of hardware based on the Whetstone
Benchmark, we present in Sections 2, 3, and 4 results using a variety
of chemistry-oriented software.  This 64-bit floating point precision
FORTRAN-based code may be classified into three distinct categories,
each designed to provide a pointer to the relative hardware
capabilities in the discipline of computational chemistry;

1. The first category (the MATRIX Benchmark, section 2) reflects the
dependence of many of the algorithms in the area of electronic
structure calculations on matrix operations, and includes both matrix
multiplication and matrix diagonalization;

2. The second category (the Computational Chemistry Kernels, section 3)
includes four chemistry `kernels', each comprising less than a 1000
lines of FORTRAN code, and intended to be representative of the typical
calculations undertaken in the area of computational chemistry.
Described in more detail in section 3, these kernels include
direct-SCF, molecular dynamics (MD), quantum monte carlo (QMC), and a
Jacobi eigen solver (JACOBI);

3. Finally, we include complete quantum chemistry applications (section
4), using the GAMESS-UK electronic structure program [3].  Twelve
typical applications are included, featuring both conventional Hartree
Fock self-consistent field (SCF) and direct SCF, complete active Space
SCF (CASSCF) and multiconfiguration SCF (MCSCF), configuration
interaction calculations, both direct-CI and conventional table-driven
MRD-CI, Moller Plesset perturbation theory (MP2), and both SCF and MP2
analytic 2nd derivatives.

2. The MATRIX Benchmark

2.1 Whetstone Benchmark

A comparison of the single processor Whetstone performance on a variety
of machines, including vector supercomputers, minisupers,
superworkstations and workstations, together with that obtained on a
single node of various novel architecture machines is given in Table
1.  Data provided includes the Mflop performance on a variety of
floating point vector loops (VL=1024), together with the total cpu time
to execute the benchmark, and the MWips performance.  The primary aim
of this benchmark is to provide a performance measure of both floating
point (FP) and integer arithmetic; thus while trends in the VL Mflop
ratings are of interest, only a small part of the total CPU time is
actually involved in these operations. The wide variety of standard
functions exercised (abs, sqrt, exp, alog, sin, cos, atan etc.) consume
a far larger fraction of the reported times; note the latter provide a
close mapping onto the measured rate of instruction processing (MWips,
million whetstones instructions per second).

This benchmark was originally designed to monitor the performance of
vector supercomputers, and an examination of Table 1 reveals that both
the Cray Y-MP and YMP-C90 continue to outperform all other machines.
As expected, the Cray YMP-J90 is less impressive, some four times
slower than the C90, and slower than five of the leading workstation
CPUs.  The fastest CPU is seen to be the 195 MHz R10000 processor from
SGI, some 1.5 times faster than the 333 MHz EV5 of the alpha 600/5.
Both CPU time and MWips rate suggest that the latter processor is
marginally faster than the recently released PA8000 processor of the HP
PA/9000-K460, and 1.5 times the speed of the 200 MHz Ultra-2/200 from
Sun. The performance of the K460 is far below that expected based on
the published SPEC-fp95 ratings, and it is clear that the compiler,
libraries etc on the machine under test (a single processor 160 Mhz
prototype of the PA8000) were not optimal, with the results of this and
subsequent benchmarks not reflecting the true potential of the PA8000.
SGI's other new processor, the R5000 from mips, is also seen to perform
well, and while about 1.8 times slower than the R10000, is faster than
the Ultra-2 and alpha 266 Mhz EV5. In contrast the R8000-based machines
>from SGI appear to under-perform, 4 times slower than the R10000, three
times slower than the AXP-600/5/333, and slower than both the HP
PA/9000-735/125 and IBM Power 2 RS/6000-3CT.  The R8000 is seen to
outperform its predecessor, the R4400, by just a factor of 1.7, based
on the CPU time for the complete benchmark.  Sun's latest processor,
the 200 MHz Ultra-2/200 is found to be more than twice the speed of the
125 Mhz HyperSPARC, and 8.5 times the 40 MHz SuperSPARC processor in
the Sun SPARC 10/41.

Considering the MPP single node performance of Table 1, the KSR-2
custom processor is seen to be comparable with mid-range workstation
CPUs (IBM RS/6000-360 and DEC AXP/3000-500), while the quality of the
FORTRAN compiler on the Cray T3D is at least in part responsible for
the Whetstone timing of 121 seconds, 1.8 times slower than the DEC
AXP/3000-500 (68.7 secs) which does, of course, house the same CPU.
The IBM-SP2 TN2 processor is by far the dominant CPU, twice the speed
of the KSR-2 and 3.5 times that of the Cray T3D.

Finally, we note that the performance of the Pentium Pro is broadly in
line with expectations. It outperforms the R8000-based SGI and
Power2-based IBM workstations, while slower than the leading CPUs from
SGI, Digital, HP and Sun, by factors of 3.8, 2.5, 2.3 and 1.7
respectively. It is important to realise that this level of performance
is only achieved using "commercial" Fortran compilers (in this case
>from Intel).  Using public domain f2c and a variety of c-compilers
produced far inferior figures, some 3-4 times slower than those of
Table 1.

2.2 Sparse Matrix Multiply Benchmark

The matrix multiply operation (MMO) is central to the efficient
operation of modern QC codes on vector processors [1], it being
possible both to extract near peak performance for this kernel and to
formulate many QC steps around this operation.  A comparison of the
single processor sparse MMO performance on a variety of machines, is
given in Table 2.  In this benchmark a series of MMOs (R = A X B)
involving matrices of order 10, 20, 30, ... 150 were performed.  Each
MMO was conducted a number of times, this number being inversely
proportional to the order of the matrices, so that the summed CPU times
of Table 2. refer to 150 MMOs of order 10 matrices, 140 of order 20
matrices, and so on up to 10 MMOs for matrices of order 150.  Figures
are presented for both `full' (0% sparse) and 50%-sparse B matrices,
with the performance figures referring to code written entirely in
Fortran.

The potential of the PA8000 processor is clearly seen in the figures of
Table 2, with the HP/PA9000-K460 recording the same time as the Cray
Y-MP/C98, and marginally faster than the R10000/195 processor. Both
processors outperform the Cray Y-MP/8128, with the HP/PA9000-K460 twice
as fast as the R8000-based SGI machines and Power2 RS/6000-3CT. The
latter machines exhibit identical performance on this benchmark (with
0% sparsity timings of 1.8 seconds). Both CPUs are marginally faster
than the EV5 600/5/333 and 84000/5/300, 1.3 times faster than the
Ultra-2/200 and 1.4 times faster than the HP PA/9000-735/125. Both
exhibit comparable timings to that on the Y-MP/8128 (1.5 seconds),
achieve some 50% of the YMP-C98 rating, and outperform the Cray YMP-J90
by a factor of 1.4.  The performance of the R5000 processor is perhaps
disappointing, four times slower than the R10000.  The R1000-based
Power Onyx is seen to outperform the corresponding R8000 machine by a
factor of 1.6, which in turn outperforms the R4400 Challenge L by a
factor of 3.9, and the earlier 50 Mhz R4000 Challenge by a factor of
5.6. Much of the speed of the R8000 may be attributed to the KAP
pre-processor, which enhances FORTRAN performance by a factor of 1.8.
The performance of the Pentium Pro/200 is again seen to be impressive,
recording exactly the same benchmark time as the DEC Alpha 600/5-266
and Sun Ultra-2/200.

Of historical note is the timing of 448.6 seconds recorded on the T800
20MHz Transputer, some 500 times slower than the PA8000 CPU and the
Cray YMP-C98.  Considering the MPP nodes, the IBM-SP2 TN2 node
outperforms the Cray AXP node of the T3D by a factor of 4.7, and the
KSR-2 by a factor of 6.6. Note that the T3D node remains 1.5 times
slower than the DEC AXP/3000-500.

One additional feature of the MMO benchmark not apparent in Table 2 is
the significantly enhanced performance found on all machines when
comparing assembly language MMO to Fortran MMO. Historically this has
often involved the user having to code key routines in assembly
language, for few vendors initially provided optimized mathematical
libraries; improvement factors of 3.2 (Cray X-MP), 4.2 (IBM 3090/VF),
3.1 (Convex C-220) and 3.4 (FPS-M64/60) have previously been reported
with assembly language implementations of the sparse MMO routine,
MXMB.  Optimized BLAS libraries are now fairly commonplace on the
majority of workstation platforms, the most notable exception, until
recently, being the SPARC offerings from Sun (note that the
Cray-optimised libraries are now available on both Hyper- and
UltraSPARC machines).  The impact of optimized library routines
continues to be evident on current workstations, with the 0% sparsity
timings of Table 2 improving by factors of 1.8, 1.9, 2.3, 2.5, 2.7 and
3.1 for the SGI R10000/195, IBM RS/6000-3CT, SGI R8000 Indigo2, HP
PA/9000-735/125, DEC Alpha 600/5/333 and Alpha 8400/5-300 respectively
when using the BLAS dgemm routine.  A corresponding factor of 3.8 is
found when using the Kuck Library on the i860, and perhaps somewhat
surprisingly, a factor of 4.5 when using SCILIB on the Cray YMP-C98.

The availability and degree of functionality of library software are,
we believe, important issues when considering cost-effective
performance.  This effect is evident from the second benchmark which,
given in Table 3, involves performing a series of similarity transforms
(Q*HQ) using both a scalar and vector algorithm. The scalar code
collapses the matrix transposition and multiplications to yield an
algorithm with fewer FLOPS than the vector code, which adopts a brute
force approach by explicitly performing the transposition and two
matrix multiplications.  In the latter case we utilize the BLAS library
routine DGEMM (where available) for performing the requisite MMOs, in
the former case the dot product BLAS routine, DDOT.

Considering the scalar algorithm, the SGI R10000 and HP PA/9000-K460
exhibit the optimum performance, with the R10000 1.1 times the speed of
the Sun Ultra-2/200 and 1.2 times that of the IBM RS/6000-3CT. The
Power2 CPU is marginally faster than the DEC 600/5/333, and 1.2 times
faster than the R8000-based SGI machines and the Sun Ultra-1/170. With
a couple of notable exceptions. this ordering is similar to that found
for the vector case, where the R10000 just outperforms the Sun
Ultra-2/200 and the DEC 600/5/333, which are in turn superior to both
the IBM RS/6000-590 and R8000-based SGI machines.  The performance of
the R10000 in the scalar algorithm is first class, faster than the Cray
Y-MP/J90, Cray Y-MP/8128 and Cray YMP C98/4256 by factors of 4.3, 2.3
and 1.2 respectively. The Pentium Pro/200 again fares well, recording
comparable scalar timings to the DEC Alpha 600/5-266, Sun Ultra-1/140,
and DEC Alpha 2100/5-250, although 1.7 times slower than the R10000.

The notably poor performance on the vector algorithm for the HP
PA/9000-K460, SGI Indy 5000 and Pentium Pro/200 may be attributed to
either use of poorly tuned maths libraries (as on the HP and SGI
machine), or to reliance on straight Fortran code (as on the Pentium).
A similar effect was seen on the RS/6000-3CT, where the relatively
unimpressive timings from the vector algorithm were caused by the
un-tuned library DGEMM routine available through -lblas; the
corresponding ESSL routine (-lessl) improves performance by a factor of
1.52 on the IBM SP2.  The Cray YMP-C98 at last justifies its
supercomputer tag, outperforming the SGI R10000, R8000 and RS/6000-3CT
by factors of 2.6, 3.2 and 3.6 respectively; the same cannot be said
for the Cray Y-MP/J90, which remains a factor of 1.7 slower than the
R10000. The latter outperforms the R5000 by factors of 3.4 (scalar) and
5.3 (vector).

As noted above all of the more recent CPUs (with the exception of the
PA/9000-K460 and Pentium Pro) exhibit superior performance on the
vector algorithm, with average factors of 2.1 (DEC Alpha 600/5-333),
2.0 (SUN Ultra-1/170), 1.8 (DEC Alpha 8400/300 and HP PA/9000-735), 1.7
(SGI R10000, SUN Ultra-2/200 and SGI R8000), and 1.6 (IBM RS/6000, with
the exception of the 590).  Much higher factors are found with the
vector CPUs; the figure of 4.2 on the Cray J90 leads to the Cray being
competitive on the vector algorithm, but slower than the leading 24
workstations on the scalar code.  Note again the inadequacies of the
FORTRAN compiler on the Cray T3D; the unexceptional scalar algorithm
timing of 79.3 secs. (to be compared with that of 45.1 secs. on the
DEC AXP/3000-500), improves significantly with the vector algorithm,
where use of the BLAS routines produces timings of 27.5, to be compared
with 23.9 secs on the AXP/3000-500.  This effect is also seen in
comparison with the KSR-2 and IBM SP2 timings; the T3D is slower by a
factor of 1.4 on the scalar algorithm, and faster by a factor of 1.3 in
the vector case compared to the KSR-2, while the differential with the
SP2 is reduced from 5.8 in the scalar case to 3.3 for the vector
algorithm.

2.3 Diagonalization Benchmark

Table 4 presents the results of a matrix diagonalization benchmark
intended to supplement the previous analysis conducted by Dunning and
co-workers [4].  We consider a similar benchmark, based on
diagonalizing a series of real symmetric matrices, with rank 10, 20,
30, ... 100, using 64-bit floating point arithmetic.  Again the CPU
time was measured for the diagonalization of each size matrix, with the
summed times used as the benchmark execution time.  Results are
presented for a range of compiler options available on the depicted
hardware.  While the previous analysis was restricted to the EISPACK RS
routine, we consider below the performance of eight diagonalization
routines available in various mathematical libraries and quantum
chemistry codes:

(i) EIGRS, an unoptimized FORTRAN version of the library routine RS
(available in SCILIB on the Cray) from the IMSL library of routines
[5].
(ii) F02ABF from the NAG library [6].
(iii) HQRII [7], as implemented in the semiempirical MOPAC program
[8].
(iv) GIVENS, adapted from the QCPE program exchange (number 62.1).
(v) SDIAG2, as implemented in the MUNICH system of programs.
(vi) JACOBI, from the ATMOL system of programs [9].
(vii) JACO, the diagonalization routine from the direct-SCF program
DISCO [10].
(viii) ERDUW, as taken from the Berkeley System of Quantum Chemistry
codes.

The first four routines are all based on the Householder QR method,
whilst the last four use the Jacobi method. Note that the only
optimization performed involved inserting calls to the BLAS for
two-dimensional rotations (DROT) and vector interchange (DSWAP).

The timings of Table 4 suggest that the SGI R10000/195 is again the
fastest CPU, just ahead of the HP PA/9000-K460 and DEC Alpha 600/5-333,
and 1.5 times faster than the Sun Ultra-2/200 and DEC Alpha
8400/5-300.  The R8000-based machines, HP/9000-735/125 and IBM
RS/6000-3CT are seen to exhibit comparable timings (8.0-8.1 secs.), a
factor of 2.5 times slower than the R10000.  This benchmark tends to be
dominated by the slowest of the diagonalization routines in use, JACO,
which typically accounts for > 40% of the total CPU time.
Significantly the leading twenty workstations are seen to outperform
the Cray YMP/C98, while the Cray Y-MP/J90 is bettered by the leading 44
workstation CPUs. The Pentium Pro is seen to be five times faster than
the J90, and is only outperformed by the leading six workstation CPUs.
The performance of the Cray T3D node is comparable to the IBM
RS/6000-350, and again significantly slower than the IBM-SP2 TN2 node
(21.7 secs. vs. 9.3 secs.)

2.4 Relative Performance on Matrix Operations

To summarize the performance of the various workstations on the matrix
multiply and diagonalization benchmarks detailed above, we show in
Table 5 the performance of each relative to the SGI R10000/195.  It is
clear from these figures that the SGI R10000 and PA8000 processor (in
the HP PA/9000-K460) lie ahead of the competition, with the R10000 1.3
times faster than the DEC Alpha 600/5-333 and 1.4 times faster than the
Sun Ultra-2/200. While the PA8000 is marginally slower than the R10000,
we belief that the arrival of tuned maths libraries on the former will
reverse this order to provide a picture more consistent with the
SPECfp95 ratings.

We see that the relative ordering of processors within a given family
are broadly in line with clock speeds.  Considering the EV5-based CPUs,
we find the DEC Alpha 600/5-333, 8400/5-300, 600/5-266 and 2100/5-250
to be slower than the R10000 by factors of 1.25, 1.49, 1.82 and 1.67
respectively. For the Sun Ultra, the Sun Ultra-2/200, Sun Ultra-1/170,
and Sun Ultra-1/140 are slower than the R10000 by factors of 1.43, 1.69
and 2.05 respectively.  We also note the following:

 -  the 266 MHz EV5-based CPU outperforms the corresponding EV4 by a
factor of 1.33;
 -  the R10000 exhibits a speed up of 1.7 against its predecessor, the
R8000 in the Power Onyx, and a speed up of 3.4 against the R5000 (due
in the main to the poor library performance on the R5000);
 -  the R8000 exhibits a speed up of 3.3 against its predecessor, the
R4400 in both the Indigo2 and Challenge L, and,
 -  the position of the Pentium Pro as the 14th fastest CPU of those
considered will undoubtedly improve given the advent of optimised
libraries (not available in this current exercise).

3. Computational Chemistry Kernels

One of the crucial requirements in evaluating the increasingly broad
range of hardware platforms, whether these be parallel machines (true
MIMD message-passing machines, workstation clusters, shared-memory
multiprocessors etc), or simply the lastest workstation, is the
availability of portable benchmarking codes that are representative of
the application area under consideration.  In an attempt to provide
such capabilities in computational chemistry, we have described
previously four representative codes, each of which is less than 1000
lines of FORTRAN, and is sufficiently portable that migration to any
hardware platform can typically be achieved in a matter of hours. In
this report we limit our discussion to the performance of these codes
on a variety of single CPUs.

The benchmarking kernels comprise the following programs that are
realistic models of actual chemical applications or algorithms;

1. Self Consistent Field (SCF); This Self Consistent Field (SCF)
electronic structure kernel uses distributed primitive 1s gaussian
functions as a basis (thus emulating use of s,p,... functions) and
computes integrals to essentially full accuracy.  It is a direct SCF
code, with an atomic density used for a starting guess.  There are two
available problem sizes, corresponding to 60 basis functions Be4 and
240 basis functions (Be16). The timings of Table 6 refer to the
former.

2. Molecular Dynamics (MD); This program bounces a few thousand argon
atoms around in a box with periodic boundary conditions.  Pairwise
interactions (Leonard-Jones) are used with a simple integration of the
Newtonian equations of motion.

3. Monte Carlo (MC); This code evaluates the energy of the simplest
explicitly correlated electronic wavefunction for the He atom ground
state using a variational monte-carlo method without importance
sampling.

4. Jacobi iterative linear equation solver (JACOBI)]; Uses a naive
jacobi iterative algorithm to solve a linear equation.  All the time is
spent in a large matrix vector product.

Total CPU timings for the SCF, MD and MC benchmarks are presented in
Table 6, together with the Mflop ratings from the JACOBI benchmark.
These results present a somewhat confusing picture, with the processor
ordering very much a function of the particular chemistry kernel under
examination. With the exception of the JACOBI benchmark, the SGI
R10000/195, DEC Alpha 600/5-333 and 8400/5-300, and Sun Ultra-2/200
processors are seen to be the superior CPUs, although the processor
ordering in the SCF, MD and MC benchmarks varies significantly.

Thus for the SCF kernel, the SGI R10000 and Alpha 600/5-333 are 1.5
times the speed of the HP PA/9000-K460, twice the speed of the Sun
Ultra-2/200 and three times that of the POWER2 RS/6000.  The
HP/9000-735/125 exhibits good relative performance - it is 1.3-1.4
times faster than the R8000 and POWER2 RS/6000 (TN2 and 3CT).  The Sun
SS20/HS21 is also seen to perform well on this kernel, with the same
execution time as the latter CPUs. The performance of the Pentium
Pro/200 matches that of the SGI R8000 and and POWER2 RS/6000.

The SGI R10000 is clearly the optimum processor in the MD benchmark,
followed by the Sun Ultra-2/200 and Alpha 600/5-333.  The POWER2 is
seen to perform very poorly in the MD Benchmark where it is apparently
almost 4.5 times as slow as the R10000, with the 3CT 3.8 times slower
than the Sun Ultra-2/200.  In fact the whole family of RS6000
processors remains consistently unimpressive on this benchmark.

The relative processor ordering found in the MD and SCF kernels is seen
to be markedly different to that suggested by the JACOBI benchmark.
The Mflop ratings of Table 6 suggest that the Power2 3CT is the optimum
CPU, with the 81 Mflop rating 2.1 times that achieved on the SGI
R10000, 2.5 times that found on the R8000 (32.9 Mflop), and 2.6 times
that recorded on the HP PA/9000-K460 (31.0 Mflop).  The Sun Ultra
performance on JABOBI is also impressive, with the Ultra-2/200, and
Ultra-1/170 and Ultra-1/140 all surpassing the MFlop rate on the EV5
and R10000 processors.

In the MC benchmark, the Alpha 600/5-333 and SGI R10000 are the fastest
processors, twice the speed of the RS/6000 POWER2 and Ultra-2/200.
Comparing the R10000/195 and R8000 processors, the R10000 is 3.2 times
faster in the SCF kernel, 2.3 in the MC kernel, but only 1.2 times
faster in JACOBI. The Indy R5000 demonstrates comparable performance to
the R8000 - it is slower than the R10000 in the SCF, MD, MC, and JACOBI
benchmarks by factors of 2.9, 2.1. 1,9 and 3.1 respectively.  The
performance of the Pentium Pro/200 is perhaps somewhat less impressive
than that found in the matrix benchmarks. Its overall performance is
similar to that shown by the DEC Alpha 250/4-266 and Indy R5000,
approximately one half the speed of the R10000.

4. The Quantum Chemistry Benchmark

The benchmark described below (and summarized in Table 7) is designed
to highlight the typical range of calculations commonly performed by
the ab initio quantum chemist. It includes 12 calculations carried out
using the GAMESS-UK electronic structure code, and includes the
following functionality;

 - Conventional SCF Calculations, on morphine and 2,4,6
tri-nitro-toluene (Calculations 1. and 2. respectively);
 - Valence-only ECP calculations, with a geometry optimization of
Na7Mg+ in an ECP-DZ+D(Mg) basis of 70 GTOs (calculation 3).
 - A Direct-SCF calculation on cytosine (82 GTOs, 6-31G basis)
Calculation 4);
 - Multi-configuration SCF calculations, with a CASSCF geometry
optimization on H2CO (Calculation 5), and a larger CASSCF calculation,
also on H2CO (Calculation 6);
 - Configuration interaction calculations, both Direct-CI on the
H2CO/H2+CO transition state (Calculation 7), and conventional table
driven-CI on TiCl4 (Calculation 8);
 - Moller Plesset calculations, with a MP2 geometry optimization of
H3SiNCO (Calculation 9);
 - Analytic second derivatives, at both the SCF (pyridine) molecule
in a 6-31G basis, Calculation 10) and MP2 level (C4) in a 6-31G* basis,
Calculation 11);
 - A Direct-MP2 calculation on pyridine in a DZ + D(N) basis set
(Calculation 12).

4.1 QC Benchmarks - Single Processor Results

The data presented in Table 8 is collected under control of the UNIX
command time where available, and includes CPU time (both user and
system), total elapsed time and Efficiency, measured as CPU versus
elapsed.  While our original aim was to base comparisons strictly on
elapsed times, such timings could not be consistently gathered over
the range of machines considered. For example, the range of disk
configurations varies enormously, from primitive SCSI disks to striped
high-speed raid disks, and the loading on the machines varies, from
effectively single-user loading on many of the workstations, to
multi-user environments, such as on the Convex.  Thus while reporting
the elapsed times, we use such figures to identify, where appropriate,
the requirement for enhanced disk configurations, rather than as any
definite criticism of the machine in question.

The total user CPU timings of Table 8 suggest that the DEC Alpha
600-5/333 and SGI R10000/195 are the optimum machines, with summed
timings of 23.4 and 23.1 minutes for all 12 calculations. These are
significantly less than those for the leading machines from Sun and IBM
which exhibit summed timings of 31.5 and 40.1 for the Sun Ultra-2/200
and RS/6000-3CT respectively.  A somewhat different picture emerges
when considering the system CPU and Elapsed times.  With the exception
of the AXP and SGI R10000, all machines exhibit a system CPU time of
the order of 10-15% of the user time; this percentage increases
significantly, particularly on the AXP, to between 20-40% on the
systems of Table 8.

Considering the elapsed times and associated efficiences. the R8000
based machines from SGI appear to be the most balanced.  Both the R8000
Power Onyx and Indigo2 exhibit efficiences of > 95%, to be compared
with figures of 76%, 64% and 59% for the RS/6000-3CT, 9000-735/125 and
Alpha 600/5-266.  What is noticeable is the significant improvements in
these efficiency ratios on the more recent Sun (Ultra-2/200) and
Digital hardware (both the DEC Alpha 600/5/333 and DEC Alpha
2100/5/250) compared to the figures recorded in the past.

Initial experience with the HP PA/9000-K460 suggested that the compiler
was too unreliable to even attempt to perform the GAMESS-UK Benchmark,
with numerous routines mis-compiling.  The poor elapsed time on the Sun
Ultra-1/140 was due in part to the limited memory on the machine (32
MByte).

Overall factors of 10.6 (in total CPU) and 13.1 (in elapsed times) are
found when comparing the ``slowest'' (Sun SPARCstation 10/30) and
``fastest'' (SGI R10000 Power Onyx) machines in Table 8.  The
corresponding CPU factors in both the Matrix and Chemistry Kernels are
somewhat higher, 18.9 and 11.2 respectively.

Considering machines from a given vendor, we find that the EV5-based
Alpha 600/5/266 outperforms the corresponding EV4 system, the 250/4/266
by factors of 1.5 (CPU) and 1.4 (elapsed). The R10000 from SG is found
to be approximately twice the speed of the R8000-based machines, and
3.2 times as fast as the Indy R5000.  The R8000-based machines in turn
are found to perform some 1.9 times faster than the corresponding Power
Challenge L and R4400 Indigo2. Significantly higher ratios are found in
some of the individual calculations of Table 7, with ratios of 2.5 -
2.8 found in the MCSCF, direct-CI, MP2 and 2nd derivative
calculations.  Two of the 12 benchmark calculations impact seriously on
the final ratios, the ECP and MRDCI calculations exhibiting negligible
speedups of 1.13 and 1.18 respectively.

5. Summary

As a summary of this work, we present in Table 9 the relative
performance of 34 of the leading workstations against the DEC Alpha
600/5/333 in terms of quoted SPEC (``Systems Performance Evaluation
Cooperative'') benchmarks, and those from the present Matrix, Chemistry
Kernels and GAMESS-UK benchmarks.  Note that this analysis has been
somewhat complicated by the inconsistent approach adopted by some
vendors to providing a smooth transition between the older SPECfp92 and
SPECint92 values, and the more recent SPECfp95 and SPECint95
benchmark.  SGI in particular appear to provide only SPECfp95 values
for the R10000 and R5000, and only SPECfp92 values for their older
processors. In the following discussion we have used the SPEC-95
results when available (see Table 9)

The SPEC benchmark suite contains non-tuned application-based code to
measure processor speed for both integer (SPECint) and floating point
(SPECfp) arithmetic. Based on the published SPECfp ratings, and
normalising with respect to the DEC Alpha 600/5/333, we would expect
the PA8000 processor of the HP PA/9000-K460 (124%) to be the fastest
CPU, followed by the DEC Alpha 600/5/333 itself, the SGI R10000/195
(94%) and DEC Alpha 8400/5/300 (94%), the DEC Alpha 600/5/266 CPU
(89%), the 200 MHz Sun Ultra-2/200 (84%), and the IBM Power2
RS/6000-3CT (77%) (where the %-values in parentheses indicate
performance relative to the Alpha 600/5/333).  Based on these relative
SPECfp values given in the table, we expect a factor of 12 between the
fastest and slowest processor, the Sun SPARC/10-30.  A somewhat
different processor ordering is revealed by the SPECint ratings, with
the processors from SGI (notably the R8000) and IBM (the Power2)
significantly slower than those from DEC, Sun and the HP (PA8000). It
is perhaps worth noting that SGI have not as yet published the
SPECint95 rating for either the R10000 or R5000. We note also that the
Specint95 ratings suggest that Pentium Pro/200 is some 88% of the DEC
Alpha 600/5/333, to be compared with the smaller rating of 51% based on
SPECfp95.

When considering the results, there are several factors we wish to
consider based on the present evaluation exercise:

1. Do the SPECfp values provide a reliable metric for evaluating the
capabilities of hardware in computational chemistry? If this so, we
would expect to find a close mapping of the ratios for the various
chemistry benchmarks onto the SPECfp ratios (note that the CPU values
for the GAMESS-UK benchmark are used, since SPEC does not adequately
incorporate I/O in its evaluation);

2. Does any particular CPU consistently ``underperform'' based on the
SPECfp criteria? - this would manifest itself as the ratios from the
chemistry benchmarks falling below the SPECfp ratios;

3. Do the ``simple'' Matrix and Chemistry Kernel benchmarks lead to the
same conclusions as the GAMESS-UK benchmarks?

In terms of relative speed, we find that all the chemistry benchmarks
are broadly in line with the SPECfp predictions, the only notable
exceptions being summarised below:

 - The poor performance of the HP PA/9000-K460 - while the matrix
kernels are in line with the SPECfp ratio, the chemistry kernels would
appear to be running at around half the expected speed.

 - The impressive performance of the SGI R10000 on all the benchmarks,
with figures of 130%, 104% and 116% on the matrix, kernels and
GAMESS-UK benchmarks, as against the value of 94% based on the SPECfp95
figures. Indeed, the R10000 would certainly appear to be the optimum
CPU based on the benchmarks conducted in this report. The R5000
appears, however, to follow closely the SPECfp95 ratings.

 - There is some evidence from Table 9 that neither the DEC EV5-based
Alpha 600/266 or the 8400/300 are performing as well as the SPEC
ratings might suggest, with all benchmark ratios some 10% lower than
expected based on SPECfp alone. In contrast the DEC Alpha 2100/5/250 is
performing consistently above its SPEC rating.

 - The UltraSPARC systems from Sun appear to be performing exactly in
line with the SPECfp95 ratings.

 - The R8000-based systems perform well on the matrix benchmarks, but
are closer to the SPECfp ratings on the kernels and GAMESS-UK.

 - All IBM Power1 RS/6000 CPUs exhibit enhanced performance on the
chemistry codes relative to the SPEC rankings e.g.. the SPECfp ratio of
the RS/6000-370 to DEC 600/5 is 22%, to be compared with the Matrix,
Kernels and GAMESS-UK ratios of 30%, 37% and 36% respectively.

 - A similar effect is shown with the HP PA/9000-735/125, where the
SPECfp ratio of 35% increases to 54%, 40% and 52% for the chemistry
benchmarks.

 - The potential of the Pentium Pro is evident, with the performance in
the Matrix benchmarks exceeding the SPECfp95 figures.

References

[1] M.F. Guest and S. Wilson, Daresbury Laboratory Preprint,
DL/SCI/P290T; Supercomputers in Chemistry, ed. P.Lykos and I.Shavitt,
A.C.S. Symposium series 173 (1981) 1; V.R. Saunders and M.F. Guest,
Comp.Phys.Comm., 26 (1982) 389:  M.F. Guest, in ``Supercomputer
Simulations in Chemistry'', Ed. M. Dupuis, Lecture Notes in Chemistry,
44, Springer Verlag (1986) 98.

[2] M.F. Guest, R.J. Harrison, J.H. van Lenthe and L.C.H. van Corler,
``Computational Chemistry on the FPS-X64 Scientific Computers:
Experience on single- and multi-processor systems'', Theoret. Chim.
Acta 71 (1987) 117.

[3] GAMESS-UK is a package of ab initio programs written by M.F. Guest,
J.H. van Lenthe, J. Kendrick, K. Schoeffel and P. Sherwood, with
contributions from R.D. Amos, R.J. Buenker, M. Dupuis, N.C. Handy, I.H.
Hillier, P.J. Knowles, V. Bonacic-Koutecky, W. von Niessen, R.J.
Harrison, A.P. Rendell, V.R. Saunders, and A.J. Stone.  The package is
derived from the original GAMESS code due to M. Dupuis, D. Spangler
and J. Wendoloski, NRCC Software Catalog, Vol. 1, Program No. QG01
(GAMESS), 1980.

[4] R. Shepard, R.A. Bair, R.A. Eades, A.F. Wagner, M.J. Davis, C.B.
Harding and T.H. Dunning Jr., Int. J. Quant. Chem. , (1983) 17; R.A.
Bair and T.H. Dunning Jr., J.Comp.Chem., 5 (1984) 44; R. Bair,
``FPS-164 Matrix Multiplication Subroutine Guide'', Argonne National
Laboratory, (1984); T.H. Dunning Jr. and R.A. Bair, ``Advanced Theories
and Computational Approaches to the Electronic Structure of
Molecules'', NATO ASI Series, D. Reidel, 1984, p1.

[5] IMSL Program Library, 1978.

[6] NAG Fortran Library, Numerical Algorithms Group Ltd, 1984.

[7] Y. Beppu, Computers and Chemistry, 6 (1982).

[8] J.P. Stewart, ``MOPAC - A General Molecular Orbital Package'', QCPE
455, 1984.

[9] V.R. Saunders and M.F. Guest, ``ATMOL3 Part 9'', RL-76-106, 1976;
M.F. Guest and V.R. Saunders, Mol.Phys., 28 (1974) 819; D. Moncrieff
and V.R. Saunders, ``ATMOL-Introduction Notes'', UMRCC, May, 1986;
Cyber-205 Note Number 32, UMRCC, September, 1985.

[10] J. Almlof et al, J.Comp.Chem., 3 (1982) 385.
Performance of Various Computers in Computational Chemistry

Table 1. Vector Whetstone Benchmark. Total CPU times (seconds), Mflop 
ratings (see text) and MWIP ratings

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Machine                    Mflop Ratings (VL=1024) Total CPU   MWIPS 
                           N2      N3      N8      (seconds) 
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
iPSC/860 (RX)             4.6     4.4     5.3       282.7      15.0
Cray T3D (AXP)            9.8     8.4     7.3       120.5      33.5
KSR-2                    32.8    31.3    29.7        68.6      59.6 
IBM SP2 (TN2 node)       49.2    38.2    49.3        35.0     116.5 
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Sun 4/370                 2.0     1.8     1.0       642.8       6.3  
SOLBOURNE S4000           1.4     1.3     0.9       629.3       6.4  
Sun SPARCstation 2/GS     4.3     3.2     1.8       366.7      11.0  
DEC S5000/120             4.5     4.0     2.7       351.3      11.5  
IBM RS/6000-320           9.4     2.4     1.3       305.3      13.3  
SGI 4D/220                5.6     4.4     2.9       289.5      14.0  
Stardent 1520             6.3     5.9     6.0       283.2      14.5 
DEC S5000/200             6.4     5.4     3.4       274.7      14.8  
SGI R3000 Indigo          6.8     3.7     3.7       233.8      17.3  
SGI 4D/320                7.6     5.9     3.6       227.0      18.0  
Sun SPARC/5-85            3.3     3.1     4.3       205.5      19.7
Stardent VISTRA-800       4.7     4.4     5.3       196.5      19.0  
SGI 4D/420                9.4     6.9     4.4       188.0      21.6  
Sun SPARC/10-30           7.0     3.4     4.0       177.2      21.0
Sun SPARC/10-41           9.4     8.1     5.3       145.0      26.5
SGI IRIS Crimson         21.8    14.3     6.1       121.7      33.7   
IBM RS/6000-540          15.1     7.7     5.7       120.3      33.8  
HP PA/9000-720           11.6    11.1     9.3       119.3      34.0  
IBM RS/6000-340          17.9     4.0     6.1       115.9      34.8
Sun SPARCserver 1000     12.5    10.9     6.5       111.6      33.8
SGI R4000 Indigo         21.8    13.6     6.4       105.8      38.1
IBM RS/6000-530H         16.4    10.4     6.8       102.0      39.9
RS/6000 PowerPC-250      15.1     8.4     5.4        95.0      38.7
IBM PowerPC-25T          15.1     8.4     6.4        93.2      41.1
HP PA/9000-730           14.0    14.2    11.5        93.4      43.4   
SGI Challenge L/100      21.8    13.6     9.1        90.8      43.7
IBM RS/6000-550          21.8    10.8     7.9        86.8      46.6  
IBM RS/6000-350          19.7     8.0     7.7        84.8      46.9
DEC AXP/3000-300         19.4    15.7    10.3        79.1      50.9 
IBM RS/6000-360          24.6     9.0     9.2        70.7      56.1
DEC AXP/3000-500         20.8    16.9    10.7        68.7      58.7 
DEC AXP/3000-600         26.2    19.8    12.7        64.4      62.8
HP PA/9000-750           15.1    27.5    24.3        64.1      63.6 
SGI R4400 Indigo^2       32.7    19.9    13.1        62.3      63.8
SGI Challenge L/150      32.8    20.5    14.2        62.9      63.3
IBM RS/6000-370          32.8    12.0    11.5        56.5      70.2
HP PA/9000-715/100       32.8    29.9    15.8        54.5      73.3
Sun SPARCstation-20/HS21 30.0    25.5    18.2        49.8      81.6
HP PA/9000-J200          39.3    32.8    33.9        41.0      99.2
HP PA/9000-755           39.3    44.4    30.9        38.9     104.7
DEC AXP/3000-700         34.1    25.6    23.6        36.5     111.1 
RS/6000 PowerPC-43P      21.9     9.8    24.2        36.4      92.2
SGI R8000 Indigo^2       27.0    26.2   109.2        36.4     112.4
SGI R8000 PowerOnyx      27.1    26.2   109.6        36.2     112.8
IBM RS/6000-590          32.8    31.3    44.2        34.8     117.3
IBM RS/6000-3CT          39.3    37.2    46.8        34.4     117.6
IBM RS/6000-3BT          39.2    37.2    47.2        34.2     118.9
Pentium Pro/200          41.8    35.2    21.7        32.3     123.7
HP PA/9000-735/125       39.3    57.3    38.9        30.8     132.0 
DEC Alpha 250/4-266      36.6    34.8    72.5        26.9     150.5
Sun Ultra-1/140          19.9    19.3   170.9        26.3     155.1
Sun Ultra-2/200          29.8    27.0   239.6        18.7     218.2
DEC Alpha 2100/5-250    143.9    39.4   107.4        17.0     238.1
DEC Alpha 600/5-266      83.9    83.9   126.3        15.8     256.1
DEC Alpha 8400/5-300     94.4    97.9   133.5        14.2     286.7   
HP PA/9000-K460         196.6   196.6   190.5        13.8     298.3 
DEC Alpha 600/5-333     201.4    52.4   138.7        12.8     311.0   
SGI PowerOnyx 10000/195 118.6    76.0   139.2         8.5     476.8  
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Convex C-220             21.4    17.7    15.7        59.6      70.0  
Convex C-3860            54.0    44.3    37.8        23.0     185.2  
CRAY YMP/J90            115.9   117.9   145.9        16.6     260.2 
CRAY Y-MP/8128          190.0   193.5   297.2         7.9     552.0 
CRAY YMP-C98/4256       542.1   539.3   668.7         3.9    1114.0 
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Table 2. Sparse MMO Benchmark: Total CPU times (seconds) for a series
of sparse MMOs (R = A X B, see text) implemented in Fortran.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 Machine                      Sparsity in B-Matrix
                                  0%      50%
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
iPSC/860 RX-node                 21.2     11.0 
KSR-2                            11.3      5.9  
Cray T3D AXP-node                 8.5      4.5 
IBM SP2 TN2-node                  1.8      1.1 
Solbourne S4000                  74.4     38.4  
Sun 4/370                        57.4     30.6 
DEC S5000/120                    50.7     25.9 
HP/Apollo DN10020                44.2     22.8
SGI 4D/220                       39.4     20.1
DEC S5000/200                    33.1     17.1 
SGI R3000 Indigo                 31.0     14.3 
SGI 4D/320                       27.9     14.4 
Sun SPARCstation 2/GS            27.5     14.4 
Stardent 1520                    26.6     17.0 
SGI 4D/420                       23.7     12.1 
Stardent VISTRA-800              20.4     10.6
Sun SPARCstation 10/30           16.1      7.9 
Sun SPARCstation 5/85            14.9      7.8
Stardent 3020                    14.7      9.1 
IBM RS/6000-320                  14.6      7.1  
SGI R4000 Indigo                 12.6      6.4 
SPARCstation 10/41               11.8      6.1 
SGI IRIS Crimson                 11.0      5.6 
SGI Challenge L/100              10.0      4.9 
IBM RS/6000-530                   9.3      4.9  
Sun SPARCserver 1000              9.3      4.7 
IBM PowerPC-25T                   9.2      4.3 
RS/6000 PowerPC-250               9.1      4.4 
IBM RS/6000-340                   8.9      4.1 
HP PA/9000-720                    8.5      4.8  
IBM RS/6000-530H                  7.8      4.1 
IBM RS/6000-350                   7.6      3.6 
SGI R4400 Indigo^2                7.1      3.4 
SGI Challenge L/150               7.1      3.4 
HP PA/9000-730                    6.7      3.5  
IBM RS/6000-360                   6.4      3.1
DEC AXP/3000-300                  6.1      3.3 
DEC AXP/3000-500                  5.7      2.9 
IBM RS/6000-550                   5.6      3.1 
HP PA/9000-750                    5.1      2.7 
IBM RS/6000-370                   5.1      2.4 
DEC AXP/3000-600                  5.0      2.6 
RS/6000 PowerPC-43P               4.3      2.0 
HP PA/9000-715/80                 3.7      2.0
DEC AXP/3000-700                  3.7      1.8 
Sun SPARCstation 20/HS21          3.5      1.8  
Sun Ultra-1/140                   3.4      1.7 
DEC Alpha 250/4/266               3.2      1.6 
HP PA/9000-755                    3.1      1.7 
HP PA/9000-715/100                3.0      1.6 
Sun Ultra-1/170                   2.8      1.4 
DEC Alpha 2100/5/250              2.6      1.3 
HP PA/9000-735/125                2.5      1.3 
Sun Ultra-2/200                   2.3      1.2 
DEC Alpha 600/5-266               2.3      1.2 
Pentium Pro/200                   2.3      1.2 
HP PA/9000-J200                   2.1      1.1 
DEC Alpha 8400/5-300              2.1      1.1 
IBM RS/6000-3BT                   2.1      1.1  
IBM RS/6000-590                   1.9      1.0 
DEC Alpha 600/5-333               1.9      1.0 
SGI R8000 Indigo^2                1.8      1.1 
SGI R8000 Power Onyx              1.8      1.1  
IBM RS/6000-3CT                   1.8      1.0  
SGI PowerOnyx 10000/195           1.1      0.6  
HP PA/9000-K460                   0.9      0.5 
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Alliant FX2808 (1CE)             17.2      9.3  
FPS-M64/60                       17.1      8.9 
Convex C-220                     10.6      6.5  
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
IBM 3090-600-E/VF                11.3      6.0 
Convex C-3860                     5.2      3.3   
Cray X-MP/416                     2.8      1.8  
Cray YMP/J90                      2.6      1.8  
Cray Y-MP/8128                    1.5      0.9  
CRAY YMP C98/4256                 0.9      0.6
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Table 3. Sparse MMO Benchmark: Total CPU times (seconds) for a series
of Similarity Transformations (H=Q*HQ, see text) using both Scalar and
Vector Algorithms.

Machine                              Algorithm
                                Scalar    Vector 
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
T800-20                         5176.0     4439.0
iPSC/2 SX-node                  3809.6     4456.1
Meiko MK086 node                 240.1      262.2 
iPSC/860 RX-node                 118.8       60.1 
KSR-2                             55.3       34.8  
Cray T3D AXP-node                 79.3       27.5  
IBM SP2 TN2-node                  13.8        8.5 
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
SOLBOURNE S4000                  711.9      750.2  
Dec S5000/120                    710.2      724.6 
Sun 4/370                        615.9      609.6  
Dec S5000/200                    368.3      445.1 
SGI 4D/220                       344.8      440.3 
Sun SPARCstation 2/GS            333.3      394.0        
SGI R3000 Indigo                 285.0      356.4 
SGI 4D/320                       245.5      329.5 
HP/Apollo DN10020                273.8      245.9 
Stardent 1520                    236.9      252.8 
SGI 4D/420                       200.1      273.8 
Stardent VISTRA-800              177.0      209.4
Stardent 3020                    160.4      144.2 
Sun SPARCstation 10/30           141.5      162.3  
Sun SPARCstation 10/41           111.3      119.3  
Sun SPARCstation 5/85            105.9      151.6 
Sun SPARCserver 1000              88.8       92.6  
SGI Indigo R4000                  98.2       78.7 
SGI IRIS Crimson                  94.2       78.7   
IBM RS/6000-320                  139.0       73.3 
IBM PowerPC-25T                   88.2       68.9 
RS/6000 PowerPC-250               92.5       68.7 
HP PA/9000-720                   124.7       66.5   
SGI Challenge L/100               74.9       58.2 
HP PA/9000-730                    89.9       48.4   
IBM RS/6000-530                   96.3       46.9 
IBM RS/6000-340                   70.4       43.4 
HP PA/9000-750                    58.6       41.5 
SGI Indigo^2 R4400                52.3       39.8
SGI Challenge L/150               56.5       39.0
IBM RS/6000-540                   66.9       38.4 
IBM PowerPC-43P                   44.3       36.4 
Sun SPARCstation 20/HS21          42.2       35.1 
IBM RS/6000-350                   55.8       34.8 
HP PA/9000-715/80                 52.7       34.4
DEC AXP/3000-300                  61.0       34.0 
IBM RS/6000-530H                  58.8       34.0 
SGI Indy R5000                    34.7       32.1
HP PA/9000-715/100                47.0       29.5 
IBM RS/6000-360                   48.0       29.3
IBM RS/6000-550                   48.3       27.7 
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
DEC AXP/3000-500                  45.1       23.9
HP PA/9000-735                    34.8       20.0
IBM RS/6000-370                   37.6       23.3
DEC AXP/3000-600                  38.5       20.2
HP PA/9000-755                    35.6       20.1
Pentium Pro/200                   17.1       23.2
HP PA/9000-J200                   33.5       16.2
IBM RS/6000-3BT                   30.8       16.2
HP PA/9000-735/125                29.2       16.2
DEC AXP/3000-700                  28.3       16.2
DEC Alpha 250/4-266               24.2       13.1
HP PA/9000-K460                   10.9       12.0
DEC Alpha 600/5-266               17.7       10.2
IBM RS/6000-3CT                   12.6        9.7
Sun Ultra-1/140                   17.1        9.5
SGI R8000 Indigo^2                15.2        8.7
SGI R8000 Power Onyx              15.1        8.7
DEC Alpha 2100/5-250              17.7        8.2
Sun Ultra-1/170                   15.5        7.9
DEC Alpha 8400/5-300              13.8        7.9
Sun Ultra-2/200                   11.5        6.8
DEC Alpha 600/5-333               13.2        6.2
SGI PowerOnyx 10000/195           10.2        6.1 
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Alliant FX2800 (1CE)             243.1       86.3
FPS-M64/60                       141.2       50.8
CONVEX C-220                     128.6       49.0
CONVEX C-3860                     55.1       20.1
Cray YMP/J90                      44.1       10.6
Cray Y-MP/8128                    23.2        5.7
Cray YMP C98/4256                 12.6        2.6
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Table 4. Matrix Diagonalization Benchmark. Total CPU times (seconds)
for a series of Matrix Diagonalizations (see text) using eight
Different Routines.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Machine                   CPU Time       Compiler
                          (seconds)      Options 
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
T800-20                    1100.5               
iPSC/2 (SX)                1059.0      -OLM     
MK086 i860                  66.8       -OLM     
iPSC/860 (RX)               62.3       -O3       
KSR-2                       27.3       -O2       
Cray T3D (AXP)              21.7       -O        
IBM SP2 (TN2)                9.3       -O3       
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Stardent 1520              255.0       -O2     
Sun 4/370                  219.9       -O      
SOLBOURNE S4000            169.0       -O3     
DEC S5000/120              145.8       -O2     
Sun SPARCstation 2/GS      103.3       -O      
SGI 4D/220                  97.4       -O2      
Apollo DN10020              96.2       -O       
DEC S5000/200               90.6       -O2       
SGI R3000 Indigo            78.8       -O2      
Stardent 3020               68.1       -O2      
SGI 4D/320                  67.2       -O2      
Stardent VISTRA             59.2       -O3      
SGI 4D/420                  58.1       -O2      
IBM RS/6000-320             46.4       -O        
Sun SPARCstation 10/30      42.2       -O -dalign  
Sun SPARCstation 10/41      35.9       -O -dalign  
IBM RS/6000-530             35.6       -O           
Sun SPARCstation 5/85       32.4       -O -dalign  
HP PA/9000-720              31.9       -O           
IBM RS/6000-540             30.8       -O           
SGI IRIS Crimson            27.6       -sopt       
IBM RS/6000-340             27.6       -O          
IBM RS/6000-530H            26.0       -O          
SGI R4000 Indigo            26.0       -O -mips2   
RS6000 PowerPC-250          25.1       -O          
Sun SPARCserver 1000        24.7       -O -dalign  
HP PA/9000-730              24.3       -O           
IBM PowerPC-25T             24.0       -O3        
IBM RS/6000-550             22.2       -O         
IBM RS/6000-350             21.3       -O         
HP PA/9000-750              20.8       +O3       
SGI Challenge L/100         20.4       -O -mips2  
IBM RS/6000-360             17.7       -O         
HP PA/9000-715/80           15.9       +O3        
SGI Challenge L/150         15.6       -O -mips2   
DEC AXP/3000-300            15.5       -O          
SGI R4400 Indigo^2          15.2       -O -mips2   
DEC AXP/3000-500            14.9       -O          
IBM RS/6000-370             14.2       -O3 
HP PA/9000-715-100          12.8       +O3                      
Sun SS20/HS21               12.4       -O -dalign        
Sun SPARCstation 20/HS21    12.4       -O -dalign        
DEC AXP/3000-600            12.1       -O                        
IBM PowerPC-43P             11.2       -O3 qarch=ppc   
HP PA/9000-735              10.0       +O3                       
HP PA/9000-755              10.2       +O3                       
HP PA/9000-J200             9.6        +O4                         
IBM RS/6000-3BT             9.4        -O3 qarch=pwr2   
IBM RS/6000-590             9.0        -O3 qarch=pwr2   
DEC AXP/3000-700            8.7        -O                           
IBM RS/6000-3CT             8.1        -O3 qarch=pwr2   
HP PA/9000-735/125          8.1        +O3                          
SGI R8000 Indigo^2          8.0        -O3 -mips4            
SGI R8000 Power Onyx        8.0        -O3 -mips4            
SGI Indy R5000              7.7        -O3 -mips4            
DEC Alpha 250/4-266         7.3        -fast                      
Sun Ultra-1/140             6.2        -fast -O4              
DEC Alpha 600/5-266         5.6        -fast                      
Sun Ultra-1/170             5.4        -fast -O4              
Pentium Pro/200             5.3        -G6 -O2                  
DEC Alpha 2100/5-250        5.2        -fast                      
DEC Alpha 8400/5-300        4.6        -fast                      
Sun Ultra-2/200             4.5        -fast -O4              
DEC Alpha 600/5-333         3.9        -fast                      
HP PA/9000-K460             3.5        +Oaggressive        
SGI PowerOnyx 10000/195     3.1        -O3 -mips4 etc    
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Convex C-220               86.5        -O2
Alliant FX2808             99.5        -Og 
FPS-M64/60                 80.7        OPT3
Convex C-3860              36.0        -O2
Cray X-MP4/16              21.3  
Cray YMP/J90               26.7  
Cray Y-MP4/64              16.0  
Cray YMP C98/4256           9.9  
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Table 5. The Matrix Benchmark: Performance relative to the SGI
         Power Onyx R10000/195

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Machine                      MMO       MMO    Diagonal       Total 
                          (FORTRAN)   (Q*HQ)  -ization
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
SGI R10000/195               100%     100%     100%          100% 
HP PA/9000-K460              123%      57%      90%           90% 
DEC Alpha 600/5-333           61%      99%      80%           80% 
Sun Ultra-2/200               50%      90%      70%           70% 
DEC Alpha 8400/5 300          55%      78%      68%           67% 
DEC Alpha 2100/5 250          44%      75%      60%           60% 
Sun Ultra-1/170               41%      78%      58%           59% 
SGI R8000 Power Onyx          63%      71%      39%           58%  
SGI R8000 Indigo^2            63%      71%      39%           58%  
IBM SP2 (TN2 node)            63%      72%      35%           57% 
DEC Alpha 600/5-266           50%      60%      56%           55% 
IBM RS/6000-3CT               63%      64%      38%           55%
Sun Ultra-1/140               33%      64%      50%           49% 
Pentium Pro/200               50%      36%      59%           48% 
HP/9000-J200                  55%      38%      32%           42% 
IBM RS/6000-3BT               54%      38%      33%           42% 
DEC Alpha 250/4-266           36%      47%      43%           42% 
HP PA/9000-735/125            46%      38%      39%           41%
Cray YMP/J90                  44%      58%      12%           38% 
DEC AXP/3000-700              31%      38%      36%           35%  
HP PA/9000-755                37%      31%      31%           33% 
SGI Indy R5000                25%      22%      41%           29%  
HP PA/9000-715/100            38%      21%      34%           28% 
DEC AXP/3000-600              23%      30%      26%           26% 
Sun SparcStation-20/HS21      33%      17%      25%           25%
IBM PowerPC-43P               27%      17%      28%           24% 
IBM RS/6000-370               22%      26%      22%           24% 
HP PA/9000-715/80             31%      18%      20%           23%
DEC AXP/3000-500              20%      26%      21%           22% 
IBM RS/6000-360               20%      21%      18%           20% 
DEC AXP/3000-300              19%      18%      20%           19% 
IBM RS/6000-550               20%      21%      14%           19% 
HP PA/9000-750                22%      15%      15%           18% 
SGI R4400 Indigo^2            16%      15%      21%           17% 
SGI Challenge L/150           16%      15%      20%           17% 
Cray T3D AXP                  13%      22%      14%           16% 
IBM RS/6000-350               15%      18%      15%           16% 
IBM RS/6000-340               13%      14%      11%           13% 
SGI Challenge L/100           11%      11%      15%           12% 
IBM PowerPC-25T               12%       9%      13%           12%  
Sun SPARCserver-1000          12%       7%      13%           11% 
HP PA/9000-720                13%       9%      10%           11% 
SGI R4000 Indigo               9%       8%      12%           10% 
Sun SparcStation-10/41        10%       6%       9%            8% 
Sun SparcStation-5/85          8%       6%      10%            8% 
IBM RS/6000-320                8%       8%       7%            8% 
Sun SparcStation-10/30         7%       4%       7%            6% 
Stardent VISTRA                6%       3%       5%            5% 
SGI 4D/420                     5%       3%       5%            4% 
SGI 4D/320                     4%       3%       5%            4% 
SGI R3000 Indigo               4%       2%       4%            3% 
Sun SPARCstation-2             4%       2%       3%            3% 
DEC S5000/200                  3%       2%       3%            3% 
Stardent 1520                  4%       3%       1%            3% 
Apollo DN10020                 3%       2%       3%            3% 
SGI 4D/220                     3%       2%       3%            3% 
DEC S5000/120                  2%       1%       2%            2% 
Solbourne S4000                2%       1%       2%            1%  
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Table 6. Computational Chemistry Kernels

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Machine                        Total CPU time (secs)  Mflop
                               =====================
                                SCF       MD     MC  Jacobi
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Sun SPARCstation 10/30          758     2214    299     6.9 
Sun SPARCstation 10/41          665     1788    266     6.6 
Sun SPARCstation 5/85          1036     1082    195     6.7
Sun SPARCserver 1000            441      783    148     6.7 
RS6000 Power-PC 250             603     1322    149    15.6 
IBM RS/6000-530H                649     1594    176    26.7  
IBM RS/6000-340                 692     1608    187    21.2 
IBM Power-PC 25T                409     1322    145    15.6 
SGI Challenge L/100             400      794    130     9.5 
SGI R4000 Indigo                375      809    112     9.5 
DEC AXP/3000-300                427      716     98    12.0
IBM RS/6000-350                 523     1288    141    27.4  
HP PA/9000-750                  237      554    163    11.5 
%IBM RS/6000-550                563     1266    149    39.9 
IBM RS/6000-360                 433     1071    117    35.1 
HP PA/9000-715/80               220      427    133    17.1 
SGI Challenge L/150             233      517     78    13.3   
SGI R4400 Indigo^2              234      523     78    13.7   
DEC AXP/3000-600                314      541     79    21.6 
HP 9000/715-100                 177      354    107    17.3 
IBM Power-PC 43P                135      470     56    14.8 
IBM RS/6000-370                 344      854     93    44.2 
HP PA/9000-J200                 121      292     92    12.4 
Sun SPARCstation 20/HS21        132      319     84    16.3 
HP PA/9000-755                  131      284    102    18.6 
DEC AXP/3000-700                146      411     54    21.7 
HP PA/9000-735/125              103      236     91    15.0 
SGI Indy R5000                  124      219     42    12.5 
SGI R8000 Indigo^2              139      218     49    23.7   
Pentium Pro/200                 142      321     38    28.4 
SGI Power Onyx R8000            138      218     49    32.9   
DEC Alpha 250/4/266              79      272     37    20.9
IBM/RS6000-3BT                  140      389     43    44.8 
Sun Ultra-1/140                 110      186     61    45.2  
IBM RS/6000-590                 146      453     43    86.0  
Sun Ultra-1/170                  98      146     58    47.3  
DEC Alpha 2100/5/250             59      187     28    27.3
IBM SP2 TN2-node                138      383     43    68.6  
HP PA/9000-K460                  68      138     31    31.0 
DEC Alpha 600/5/266              57      210     31    40.9
IBM RS/6000-3CT                 138      462     42    81.1  
Sun Ultra-2/200                  82      121     49    56.5  
DEC Alpha 8400/5/300             50      183     27    43.9 
DEC Alpha 600/5/333              46      137     21    44.9 
SGI PowerOnyx 10000              43      106     22    39.1 
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
CONVEX C-220                   1015     1017    329    33.1  
CONVEX C-3860                   453      342    141    69.9 
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Table 7. The GAMESS-UK Single Processor Benchmark
 
Number Module            Basis (GTOs)      Details   Molecular 
                                                     Species 
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
1.     SCF               STO-3G (124)                Morphine
2.     SCF               6-31G (154)                 C6H3(NO2)3
3.     ECP Geometry      ECPDZ (70)                  Na7Mg+
       Optimization 
4.     Direct-SCF        6-31G (82)                  Cytosine
5.     CASSCF            TZVP  (52)        480 csf   H2CO
       Geometry Opt. 
6.     MCSCF             (5s3p2d/3s1p/f(O)  5608     H2CO
                           (74)
7.     Direct-CI         (5s3p2d/3s1p)    3M/167194  H2CO/H2+CO TS
                           (64)
8.     Table-CI (26M/6R) ECP  (59)      2301815/4097 TiCl4
9.     MP2 Geometry      6-31G*  (70)                H3SiNCO
       Optimization 
10.    SCF Second        6-31G (64)                  C5H5N
       Derivatives 
11.    MP2 Second        6-31G*  (60)                C4
       Derivatives
12.    Direct-MP2        DZ+D(N) (76)                C5H5N
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Table 8. The GAMESS-UK Benchmark: Total CPU time (user and system)
Elapsed time (minutes) and Efficiency (%)  for Calculations 1 - 12 
(see text)

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Machine                            CPU Time     Elapsed   Efficiency
                                   User  System    Time    (%)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
DEC Alpha 600/5/333                23.4    7.6     34.4    91%
SGI PowerOnyx 10000                23.1    3.6     36.7    73% 
Sun Ultra-2/200                    31.5    3.0     38.1    91% 
DEC Alpha 2100/5/250               30.2    8.2     43.6    88%
SGI R8000 Power Onyx               48.1    5.6     55.2    97%
Sun Ultra-1/170                    40.5    4.9     56.3    81% 
IBM RS/6000-3CT                    40.1    4.4     58.3    76%
SGI Indigo^2 R8000                 50.8    7.2     60.6    96%
IBM RS/6000-590                    46.6    4.7     74.8    68%
DEC Alpha 600/5/266                30.6    6.4     62.2    59%
DEC Alpha 250/4/266                46.0    9.7     85.7    65%
DEC Alpha 8400/5/300               26.9   10.4     92.8*   40%
HP PA/9000-735/125                 51.6    8.4     93.3    64%
HP PA/9000-755                     64.9    8.8     98.2    75% 
SGI Indy R5000                     72.9   11.3    101.0    83%
DEC AXP/3000-700                   53.4   11.5    105.4    62%
DEC AXP/3000-600                   72.1   14.1    107.8    80%
IBM RS/6000-370                    78.7    8.4    108.8    80% 
SGI R4400 Challenge L/150          93.3   10.3    110.6    94% 
SGI R4400 Indigo^2                 94.3   10.0    120.6    86% 
HP 9000/715-100                    81.4   14.3    124.7    77% 
Sun Ultra-1/140                    45.3    5.7    139.8*   36% 
HP PA/9000-715/80                  93.7   15.9    140.1    78%
DEC AXP/3000/500                   93.0   40.1    148.6    90% 
HP PA/9000-750                    111.1   17.4    140.2    92% 
IBM RS/6000-550                   117.6   11.2    146.4    88% 
SGI Challenge L/100               140.8   17.1    178.0    89% 
DEC AXP/3000-300                  129.8   39.6    184.0    92% 
Sun SS-20/HS21                    82.5    16.2    202.7    49% 
SGI R4000 Indigo                  153.2   17.7    206.0    83% 
Sun SPARCserver 1000              175.1   50.8    445.6    51%  
Sun SPARCstation 10/41            201.4   21.0    260.4    85%  
Sun SPARCstation 5/85             240.5   25.8    299.0    89%
Sun SPARCstation 10/30            251.4   31.7    306.3    92% 
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
CONVEX C-3860                     124.3    3.5    210.9    61% 
Cray Y-MP/8128                     56.8    6.0    188.4    33% 
Cray YMP-C98/4256                  37.9    2.0     41.2    97% 
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
* see footnotes to Table 9

Table 9. The Chemistry Benchmark: Performance relative to the 
         DEC Alpha 600/5/333 (see text)

 Machine                   SPECfp  SPECint   Matrix   CC         GAMESS-UK
                                                      Kernels    CPU     Wall
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
DEC Alpha 600/5/333           100   100        100    100        100      100
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
HP PA/9000-K460               124   113        124     76                     
SGI R10000/195                 94              130    104        116       93 
DEC Alpha 8400/5/300           94    81         85     85         83       37 *
DEC Alpha 600/5/266            89    86         71     76         84       55 
Sun Ultra-2/200                84    83         87     86         90       90 
IBM RS/6000-3CT                77    37         72     73         70       59
Sun Ultra-1/170                69    60         73     70         68       61 
DEC Alpha 2100/5/250           64    65         74     71         81       79 
Sun Ultra-1/140                60    50         61     63         61       25 +
SGI Power Onyx $               57    26         75     53         58       62 
Pentium Pro/200                51    88         64     48                     
SGI Indigo^2 R8000 $           49    27         75     48         54       57
DEC Alpha 250/4/266            48    56         53     53         56       40
DEC 3000/700 AXP $             43    40         45     38         48       32
SGI Indy R5000                 36               39     44         37       34 
HP 9000/735-125                35    43         54     40         52       37
HP 9000/755   $                31    26         43     36         42       35
DEC 3000/600 AXP $             30    28         33     29         36       17
Sun SS-20/HS21   $             28    32         34     35         31       17
DEC 3000/500 AXP               28    23         28     19         23       23
HP 9000/715-100                26    31         38     31         32       27
HP 9000/715-80  $              23    23         31     27         28       24
IBM RS/6000-370 $              22    17         30     37         36       31
DEC 3000/300 AXP $             17    16         25     20         18       19
SGI Challenge L/150  $         16    22         22     26         30       31
SGI Indigo^2 R4400 $           16    22         23     26         30       28
SPARC SS-1000 $                15               14     14         14        8
HP 9000/750   $                14    12         24     21         24       24
IBM RS/6000-550 $              13     9         24     31         24       23
SGI Challenge L/100 $          12    15         16     17         20       19
SGI Indigo R4000 $             11    14         13     17         18       17
Sun SS-10/41                   10    12         11      9         14       13
Sun SS-5/85  $                 10    16         10     11         12       11
Sun SS-10/30  $                10    11          8      9         11       11 
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

$ - SPECfp and SPECint rations based on SPEC92 values.
* - multi-user environment on  DEC Alpha 8400/5/300.
+ - small memory configuration (32 MByte) on Sun Ultra-1/140.

Table 10. APPENDIX I: Machine Configurations under Evaluation

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 Machine                   Configuration              Location 
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                           Workstations  
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 Solbourne S4000                                      DL (loan) 
 Sun 4/370                                            DL   
 Sun SPARCstation 2/GS      SPARC/40 Mhz              DL (loan)  
 Sun SPARCstation 5/85      MicroSPARC II/85 MHz      DL (loan) 
 Sun SPARCstation 10/30     SuperSPARC/36 MHz         DL (loan)  
 Sun SPARCstation 10/41     SuperSPARC/40 MHz         PNL  
 Sun SPARCserver 1000       SuperSPARC/50 MHz         DL (loan)  
 Sun SPARCstation 20/HS21   HyperSPARC/125 MHz        DL(loan)  
 Sun Ultra-1 Model 140      UltraSPARC-1/143 MHz      DL (loan) 
 Sun Ultra-1 Model 170      UltraSPARC-1/167 MHz      DL 
 Sun Ultra-2 Model 200      UltraSPARC-2/200 MHz      DL (loan)  
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 HP/Apollo DN10020          PRISM                     DL   
 HP PA/9000-720             PA7000/50 MHz             DL  
 HP PA/9000-730             PA7000/66 MHz             MCC  
 HP PA/9000-750             PA7000/66 MHz             DL   
 HP PA/9000-715/100         PA7100LC/100 MHz          DL (loan) 
 HP PA/9000-715/80          PA7100LC/80 MHz           DL (loan) 
 HP PA/9000-755             PA7100/99 MHz             DL    
 HP PA/9000-735/125         PA7150/125 MHz            PNL   
 HP PA/9000-J200            PA7200/100 MHz            DL (loan)   
 HP PA/9000-K460            PA8000/160 MHz            DL (loan)  
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 DEC S5000/120              R3000A/R3010A 20 Mhz      DL (loan)  
 DEC S5000/200              R3000A/R3010A 25 MHz      DL (loan)  
 DEC AXP/3000-300           AXP A21064/150 MHz        PNL   
 DEC AXP/3000-500           AXP A21064/150 MHz        DL (loan)    
 DEC AXP/3000-600           AXP A21064/175 MHz        PNL  
 DEC AXP/3000-700           AXP A21064A/225 MHz       DL (loan)  
 DEC Alpha 250/4/266        AXP A21064A/266 MHz       DL (loan)  
 DEC Alpha 600/5/266        AXP A21164/266 MHz        DL (loan)  
 DEC Alpha 2100/5/250       AXP A21164/250 MHz        DL (loan)  
 DEC Alpha 8400/5/300       AXP A21164/300 MHz        RAL  
 DEC Alpha 600/5/333        AXP A21164/333 MHz        DL (loan)  
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 SGI 4D/220 GTX                                       DL  
 SGI 4D/320                  R3000A/R3010A 33 MHz     DL (loan)  
 SGI 4D/420                                           DL (loan)  
 SGI IRIS Crimson           R4000/R4010 100 Mhz       DL (loan)  
 SGI R3000 Indigo           R3000A/R3010A 33 MHz      DL (loan)  
 SGI R4000 Indigo           R4000/R4010 100 MHz       DL (loan)  
 SGI Challenge L/100        R4400/R4010 100 MHz       Utrecht   
 SGI R4400 Indigo^2         R4400/R4010 150 MHz       DL (loan) 
 SGI Challenge L/150        R4400/R4010 150 MHz       Southampton  
 SGI R8000 Indigo^2         R8000/R8010 75 MHz        DL (loan) 
 SGI R8000 Power Onyx       R8000/R8010 75 MHz        DL (loan)  
 SGI Indy R5000             R5000/R5000 180 Mhz       DL (loan)  
 SGI PowerOnyx 10000        R10000/R10010 195 MHz     DL (loan)  
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 Stardent 1520                                        DL   
 Stardent 3020                                        DL (loan)  
 Stardent VISTRA-800                                  DL (loan)   
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 IBM Power1 RS/6000-320                               DL (loan)   
 IBM Power1 RS/6000-530                               DL (loan)   
 IBM Power1 RS/6000-530H     RS6000/33  MHz           DL    
 IBM Power1 RS/6000-540                               Perugia  
 IBM PowerPC-25T             MPC601 66 MHz            DL   
 IBM PowerPC-43P             MPC604 100 MHz           DL   
 IBM Power1 RS/6000-340      RS6000/33  MHz           DL (loan)   
 IBM Power1 RS/6000-350      RS6000/41.6  MHz         DL (loan)   
 IBM Power1 RS/6000-550      RS6000/41.6  MHz         Perugia  
 IBM Power1 RS/6000-360      RS6000/50  MHz           DL (loan) 
 IBM Power1 RS/6000-370      RS6000/62.5  MHz         DL   
 IBM Power2 RS/6000-590      RS6000/66 MHz            IBM 
 IBM Power2 RS/6000-3BT      RS6000/67 MHz            DL (loan) 
 IBM Power2 RS/6000-3CT      RS6000/72 MHz            DL (loan) 
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                             PCs
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 Netpower PC                 Pentium Pro/200Mhz       DL (loan) 
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                             SuperMinis 
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 Alliant FX2808                                       DL   
 FPS-M64/60                                           DL   
 Convex C-220                                         DL  
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                             SuperComputers 
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 Convex C-3860                                        ULCC
 IBM 3090-600-E VF                                    RAL
 Cray YMP J90/10                                      EPCC
 Cray Y-MP/8128                                       SARA
 Cray YMP C98/4256                                    SARA 
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                             Novel architecture Node
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 Meiko Computing Surface     T800-20                  DL
 iPSC/2                      SX-node                  DL
 iPSC/2                      VX-node                  DL
 iPSC/860                    RX-i860 node (40 MHz)    DL
 KSR-2                       KSR-2 node (80 MHz)      PNL
 Cray T3D                    AXP node (150 MHz)       Edinburgh
 IBM SP2                     TN2 node (67 MHz)        DL
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 =========     =========     =========    ========   ******  ******

_______________________________________________________________________

 Carles Colominas
 Dept. of Org. Chem.                E-mail     [email-masked]
 Institut Quimic de Sarria.         TEL:       (34-3)-203.89.00
 Universitat Ramon Llull.           FAX:       (34-3)-205.62.66
 Via Augusta 390. 
 08017-Barcelona. CATALONIA.
_______________________________________________________________________

>From [email-masked] Tue Oct 22 01:40 EDT 1996
Date: Tue, 22 Oct 1996 13:37:52 +0800 (CST)
From: Guo Jian-Xin <[email-masked]>
To: [email-masked]
Subject: M:Force constant in MOPAC6?

Dear Netters:
    I found there are diagonal elements in the force constant 
matrix in the output of MOPAC 6.0, for example, it gives:

force constant:

         O     C    H  ........
   O    3.0   
   C    2.5   2.0  
   H    3.7   1.8  3.3
   .     .     .    .
   .

I wonder what the meaning is for the diagonal element? (In Gaussian9X, 
I can not see the similar result, the force constant were given for each 
mode) 
    Another question is the force constant matrix is connected with the 
normal modes. whether there exist the similar "force constant matrix" 
connected with the internal coordinates? I know the normatl modes can be 
transformed from the internal coordinates, are there any methods to get 
the transformed matrix in MOPAC6 or any other direct method to calculate 
the force constant?
   Thanks in advances.
   I will summary the replies if interested.

Guo