Summary:Benchmarks



 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
  =========     =========     =========    ========   ******  ******
 From: Steen Hammerum <steen -8 at 8- kiku.dk>
 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 (roberto -8 at 8- boston.sgi.com) 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 (j.brodholt -8 at 8- ucl.ac.uk) 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 (billings -8 at 8- helix.nih.gov) 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 (gmcenroe -8 at 8- crl.com) 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                                           steen -8 at 8- kiku.dk
 Department of Chemistry                              (+45) 35 32 02 08
 University of Copenhagen, Denmark               fax: (+45) 35 32 02 12
  =========     =========     =========    ========   ******  ******
 From: desimone -8 at 8- mroa.ENET.dec.com
 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
 =========     =========     =========    ========   ******  ******
 From: DEPAZ -8 at 8- ccuam3.sdi.uam.es
 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
 =========     =========     =========    ========   ******  ******
 From:crawfordoh -8 at 8- ornl.gov
 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 netlib -8 at 8- ornl.gov, 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:  crawfordoh -8 at 8- ornl.gov
 Oak Ridge, Tennessee 37831-6123   Express delivery, add:  Bethel Valley Road
 USA
 ----------------------------------------------------------------------------
  =========     =========     =========    ========   ******  ******
 From: "M. Nicklaus" <mn1 -8 at 8- helix.nih.gov>
 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: mn1 -8 at 8- helix.nih.gov               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
 ------------------------------------------------------------------------
  =========     =========     =========    ========   ******  ******
 From: Vikram Varma <varma -8 at 8- nrcbs8.bio.nrc.ca>
 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: varma -8 at 8- nrcbs8.bio.nrc.ca
 Ottawa, Ontario K1A 0R6			   www: http://nrcbsa.bio.nrc.ca/~varma
 <<<<<
  =========     =========     =========    ========   ******  ******
 From: Alexander Hofmann <hofmann -8 at 8- pctc.chemie.uni-erlangen.de>
 Some Gaussian-benchmarks
 http://www.chem.joensuu.fi/people/juha_muilu/Misc/benchmarks.html
 regards
 alex
  =========     =========     =========    ========   ******  ******
 From: "M.F.Guest" <M.F.Guest -8 at 8- dl.ac.uk>
 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:  m.f.guest -8 at 8- dl.ac.uk *
 * 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     ccolo -8 at 8- mompou.iqs.url.es
  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.
 _______________________________________________________________________