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\begin{document}

\vspace*{2.7cm}
\begin{center}
\begin{large} 
{\bf NAS PARALLEL BENCHMARK RESULTS 10-94}\\
\end{large}
David H. Bailey, Eric Barszcz, Leonardo Dagum and Horst D. Simon$^1$ \\
NAS Technical Report NAS-94-001\\
October 1994
\end{center} 

\vspace{3ex} \noindent
{\bf Abstract}

The \footnotetext[1]{
Bailey and Barszcz are employees of NASA Ames Research Center.  Dagum
and Simon are employees of Computer Science Corp., and their work was
funded by the NASA Ames Research Center under contract NAS2-12961.
Mailing address for all authors: NASA Ames Research Center, Mail Stop
T27A-1, Moffett Field, CA 94035-1000.  The latest NPB results are
available electronically on the WWW beginning at URL address: 
{\tt http://www.nas.nasa.gov/RNR/Parallel/NPB/NPBindex.html}
or by sending an email request to {\tt leo@nas.nasa.gov}
}
NAS Parallel Benchmarks have been developed at NASA Ames Research
Center to study the performance of parallel supercomputers.  The eight
benchmark problems are specified in a ``pencil and paper'' fashion.
In other words, the complete details of the problem to be solved are
given in a technical document, and except for a few restrictions,
benchmarkers are mostly free to select the language constructs and
implementation techniques best suited for a particular system.

This paper presents performance results of various systems using the
NAS Parallel Benchmarks.  These results represent the best results
that have been reported to us for the specific systems listed.  
Some changes and clarifications to the benchmark rules are also described.  


\newpage
\section{Introduction}

The Numerical Aerodynamic Simulation (NAS) Program, located at
NASA Ames Research Center, is dedicated to advancing the science of
computational aerodynamics.  One key goal of the NAS organization is
to demonstrate by the year 2000 an operational computing system
capable of simulating an entire aerospace vehicle system within a
computing time of one to several hours.  It is currently projected
that the solution of this grand challenge problem will require a
computer system that can perform scientific computations at a
sustained rate approximately one thousand times faster than 1990
generation supercomputers.  Most likely such a computer system will
employ hundreds or even thousands of processors operating in parallel.

In order to objectively measure the performance of various highly
parallel computer systems and to compare them with conventional
supercomputers, we along with other scientists in our organization
have devised the NAS Parallel Benchmarks (NPB).  Note that the NPB are distinct
from the High Speed Processor (HSP) benchmarks and procurements.
The HSP benchmarks are used for evaluating production supercomputers
for procurement, whereas the NPB are for studying massively parallel
processor (MPP) systems not necessarily tied to a procurement.

The NPB are a set of
eight benchmark problems, each of which focuses on some important
aspect of highly parallel supercomputing for aerophysics
applications.  Some extension of Fortran or C is required for
implementations, and reasonable limits are placed on the usage of
assembly code and the like, but otherwise programmers are free to
utilize language constructs that give the best performance possible on
the particular system being studied.  The choice of data structures,
processor allocation and memory usage are generally left open to the
discretion of the implementer.

The eight problems consist of five ``kernels'' and three ``simulated
computational fluid dynamics (CFD) applications''.  Each of these is
defined fully in \cite{naspar}.  The five kernels are relatively
compact problems, each emphasizing a particular type of
numerical computation.  Compared with the simulated CFD applications,
they can be implemented fairly readily and provide insight as to the
general levels of performance that can be expected on these specific
types of numerical computations.

The simulated CFD applications, on the other hand, usually require
more effort to implement, but they are more indicative of the types of
actual data movement and computation required in state-of-the-art
CFD application codes.  For example, in an isolated kernel a certain
data structure may be very efficient on a certain system, and yet this
data structure would be inappropriate if incorporated into a larger
application.  By comparison, the simulated CFD applications require
data structures and implementation techniques that are more typical of
real CFD applications.

Space does not permit a complete description of these benchmark
problems.  A more detailed description of these benchmarks, together
with the rules and restrictions associated with the benchmarks, may be
found in \cite{npb}.  The full specification of the benchmarks is
given in \cite{naspar}.  

Sample Fortran programs implementing the NPB on a single processor
system are available as an aid to implementors.  These programs, as
well as the benchmark document itself, are available through the World
Wide Web (WWW) at URL address: 

\noindent{\tt http://www.nas.nasa.gov/RNR/Parallel/NPB/NPBindex.html}

or through postal mail from the
following address: NAS Systems Division, Mail Stop 258-6, NASA Ames
Research Center, Moffett Field, CA 94035, attn: NAS Parallel Benchmark
Codes or by sending an email request to: bm-codes@nas.nasa.gov. 
The sample codes are provided on Macintosh floppy disks and
contain the Fortran source codes, ``README'' files, input data files,
and reference output data files for correct implementations of the
benchmark problems.  These codes have been validated on a number of
computer systems ranging from conventional workstations to
supercomputers.

There are now two standard sizes for the NAS Parallel Benchmarks;
these will be referred to as the Class A and Class B size problems.
The nominal benchmark sizes for the Class A and Class B are listed in
Tables 1a and 1b respectively.  
These tables also give the standard
floating point operation (flop) counts for the two classes of
problems.  
Note that in the case of MG the grid size is unchanged,
but a greater flop count results from changes in the inner loop iterations.
We insist that those wishing to compute performance rates
in millions of floating point operations per second (Mflop/s) use
these standard flop counts.  The tables contain Mflop/s rates
calculated in this manner for the (frozen) 1992 implementation on
one processor of the Cray Y-MP for Class A and the current fastest
implementation on one processor of the
Cray C90 for Class B.  Note, however, that in Tables 2
through 9, performance rates are {\em not} cited in Mflop/s; we
present instead the actual run times (and, equivalently, the
performance ratios). We suggest that these, and not Mflop/s, be
examined when comparing different systems and implementations.

In the following, each of the eight benchmarks will be briefly
described, and then the best performance results we have received to
date for each computer system will be given in Tables 2 through 9.
These tables include run times and performance ratios.  The
performance ratios compare individual timings with the current best
time on that benchmark achieved on one processor of either a Cray Y-MP
(for Class A) or a Cray C90 (for Class B).  The
run times in each case are elapsed time of day figures, measured in
accordance with the specifications given in \cite{naspar}.

With the exception of the Integer Sort benchmark, these standard flop
counts were determined by using the hardware performance monitor on either
the Cray Y-MP or the Cray C90, and we believe that they are close to 
the minimal counts required for these problems.  In the case of the Integer Sort
benchmark, which does not involve floating-point operations, we
selected a value approximately equal to the number of integer
operations required, in order to permit the computation of performance
rates analogous to Mflop/s rates.  We reserve the right to change
these standard flop counts in the future if deemed necessary.

\begin{table} \begin{center}
\begin{tabular}{|l|l|r|r|r|}
\hline
Benchmark               & Abbrev- & Nominal & Operation        & Mflop/s \\
Name                    & iation  & Size    & Count ($\times 10^9$)& on Y-MP/1\\
\hline
\hline
Embarrassingly Parallel      & EP & $2^{28}$              & 26.68  & 211 \\
Multigrid                    & MG & $256^3$               & 3.905  & 176 \\
Conjugate Gradient           & CG & $14,000$              & 1.508  & 127 \\
3-D FFT PDE                  & FT & $256^2\times 128$     & 5.631  & 196 \\
Integer Sort                 & IS & $2^{23}\times 2^{19}$ & 0.7812 &  68 \\
LU Simulated CFD Application & LU & $64^3$                & 64.57  & 194 \\
SP Simulated CFD Application & SP & $64^3$                & 102.0  & 216 \\
BT Simulated CFD Application & BT & $64^3$                & 181.3  & 229 \\
\hline
\end{tabular}
\stepcounter{table}
\subcaption{Standard Operation Counts and YMP/1 Mflop/s for Class~A Size Problems}

\vspace{.2in}

\begin{tabular}{|l|l|r|r|r|}
\hline
Benchmark               & Abbrev- & Nominal & Operation        & Mflop/s \\
Name                    & iation  & Size    & Count ($\times 10^9$)& on C90\\
\hline
\hline
Embarrassingly Parallel      & EP & $2^{30}$              & 1008.8  & 543 \\
Multigrid                    & MG & $256^3$               & 18.81  & 498 \\
Conjugate Gradient           & CG & $75,000$               & 54.89  & 447 \\
3-D FFT PDE                  & FT & $512\times 256^2$     & 71.37  & 560 \\
Integer Sort                 & IS & $2^{25}\times 2^{21}$ & 3.150  & 244 \\
LU Simulated CFD Application & LU & $102^3$               & 319.6  & 493 \\
SP Simulated CFD Application & SP & $102^3$               & 447.1  & 627 \\
BT Simulated CFD Application & BT & $102^3$               & 721.5  & 572 \\
\hline
\end{tabular}
\subcaption{Standard Operation Counts and C90 Mflop/s for Class~B Size Problems}
\end{center} \end{table}

The NAS organization reserves the right to verify any NPB results that
are submitted to us.  We may, for example, attempt to run the
submitter's code on another system of the same configuration as that
used by the submitter.  In those instances where we are unable to
reproduce the submitter's supplied results (allowing a 5\% tolerance)
our policy is to alert the submitter of the discrepancy and allow him
or her until the next release of this report to resolve the
discrepancy.  If the discrepancy is not resolved to our satisfaction,
then our own observed results, and not the submitter's results, will
be reported.  This policy will apply to all results we receive and publish.

Whenever possible, we have tried to credit the actual individuals and
organizations who have contributed the performance results cited in
the tables.  In these citations, NAS denotes the NAS Applied Research
Branch at NASA Ames (including both NASA civil servants and Computer
Science Corp. contractors); RIACS denotes the parallel systems
division of the Research Institute for Advanced Computer Science,
which is located at NASA Ames; BBN denotes Bolt, Beranek and Newman;
BCS denotes Boeing Computer Services; CRI denotes Cray Research,
Inc.; Fujitsu denotes Fujitsu America, Inc.; KSR denotes 
Kendall Square Research Corp.; IBM denotes International Business Machines, 
Inc.; Intel denotes the
Supercomputer Systems Division of Intel Corp.; MasPar denotes MasPar
Computer Corp.; Meiko denotes Meiko Scientific Corp.; 
NEC denotes HNSX Supercomputers Inc.;
and TMC denotes
Thinking Machines, Inc.  Where no individual citation is made for a
specific model, the results are due to vendor staff.

This paper reports benchmark results on the following systems: 
TC2000 by Bolt, Beranek and Newman (BBN); 
YMP, EL, C90, and T3D by Cray Research Inc. (CRI); 
Paragon and iPSC/860 by Intel; 
SP-1, SP-2 (wide node) and RS6000-590 by International Business Machines (IBM); 
VPP500 by Fujitsu;
KSR1 and KSR2 by Kendall Square Research; 
ADENART by Kyoto University and Matsushita Electric Industrial Co.;
MP-1 and MP-2 by MasPar Computer Corp.; 
CS-1 and CS-2 by Meiko Scientific;
nCUBE-2S by nCUBE; 
SX-3 by NEC;
Power Challenge XL and Power Indigo 2 by Silicon Graphics Inc. (SGI);
CM-2, CM-200, CM-5, and CM-5E by Thinking Machines Corp. (TMC); 
and clusters of distributed workstations including
Sparcstation's by Sun; RS6000's by IBM; and 4D25's by SGI.
Entries in the tables are ordered alphabetically by vendor, except for
distributed workstation results which appear last.

Unfortunately, the limited space in this report does not permit
discussion of the methods used in any of these implementations.
However, references to technical papers describing
these methods have been included whenever such papers are available.  
In particular, details of the implementation of these benchmarks on 
the TC2000, the CM2, the CM200, the SP-1 and the IBM Cluster
may be found in \cite{tmc,bbn,ibm,sukup}.
General discussion on architectural requirements for 
the benchmarks may be found in \cite{fillo}.
Readers are referred to these documents for full details.

This report includes a number of new and/or improved 
results on the
Cray C90 and T3D, the Fujitsu VPP500, 
the Intel Paragon (with OSF1.2 and with SunMos),
the IBM wide node SP-2,
the Kendall Square KSR2,
the nCUBE-2S,
the NEC SX-3, 
and the SGI Power Challenge and Power Indigo systems.
The ``Parasoft IBM (token)'' results were run on a cluster of nine
IBM RS6000-320H workstations with 25 MHz clock rate, 16 MB memory and
a token ring interconnect capable of 16 MBits/sec transfer rates.
The performance improvements observed on some of these systems
reflect improvements both in compilers and implementations.
Efforts are currently underway to port the NAS Parallel Benchmarks on
other systems, and we hope to have more results in the future.

\section{Benchmark Changes}

Because the benchmarks are specified in only a pencil and paper fashion, it
is inevitable that loopholes develop whereby the benchmark rules are not
violated but the benchmark intent is defeated.  This section addresses
changes to be made in the Embarrassingly Parallel (EP) and 
Conjugate Gradient (CG) benchmark specification in order to
close some loopholes that have developed with these kernels.  

Eventually
we hope that parallel computing technology will advance to the point where
we will be able to measure performance by providing source code, rather 
than pencil and paper, benchmark descriptions.  However, the current lack of 
a common parallel language or architectural paradigm prohibits our movement
in this direction.  


\subsection{Changes to EP}

The intent of the EP benchmark is to provide an accuracy and performance
check on the Fortran LOG and SQRT intrinsics and to act as an easy 
kernel which vendors can readily implement on prototype systems.
There are two possible loopholes in its implementation which are
here disallowed.  Results employing these loopholes will not be reported
in future releases of this report.

The first loophole involves using a table lookup scheme to compute the
SQRT and LOG functions used to generate Gaussian pseudorandom numbers.  
When the resulting numbers are close to the histogram boundaries in the
verification test, a full precision evaluation of these intrinsics is
employed.  Thus the scheme passes all the verification tests yet defeats
the intent of this benchmark.

The second loophole involves replacing calls to the SQRT and LOG intrinsics
by a single call to a Fortran coded function that returns the SQRT(-LOG(X)).
Again this scheme will pass the verification test yet does not satisfy the
intent since the Fortran intrinsic functions have not been employed in
the implementation.

Two changes are here made to the benchmark specification.  First, two checksums
are now required as part of the verification test.  Second, only Fortran
intrinsic functions (or equivalent calls to the standard C math library)
may be used for SQRT and LOG.


\subsection{Changes to CG}

The intent of the CG benchmark is to test the performance of the system
for unstructured grid computations which by their nature require
irregular long distance communication or memory access.  The
benchmark essentially requires computing a sparse matrix-vector
product.  Rather than distribute a multi-Mbyte file for the matrix, 
the compact subroutine {\bf makea} is supplied to generate a random
sparse matrix.  The {\bf makea} procedure generates a sparse matrix by
summing outer products of random sparse vectors.
This construction is intended to preclude the clever use of {\em a priori} 
knowledge of the matrix structure to reduce the communication requirement.

Nonetheless,
by saving the random vectors used in {\bf makea}, it is possible to
reformulate the sparse matrix-vector multiply and its associated irregular
communication in a way such that communication is substantially
reduced, and only a few dense vectors are communicated. All sparse
operations can be kept local to the processing nodes.

Although this scheme of matrix-vector multiplication may be considered to
satisfy the the rules of the CG benchmark, it defeats its intended
purpose of measuring random communication performance. Therefore
this scheme is no longer allowed and results employing this loophole
will not be reported in future releases of this report. 
A strict interpretation
of the benchmark specification \cite{naspar} precludes this scheme since
it is clearly stated that the conjugate gradient method will be used to
compute the solution $z$ to $Az = x$, and as part of this method the
vector $q$ must be computed via the product $q = Ap$.  This means the
matrix $A$ must be used, not the vectors employed in its construction.


\section{Kernel Results}
\subsection{Embarrassingly Parallel (EP) Benchmark}

The first of the five kernel benchmarks is an ``embarrassingly
parallel'' problem.  In this benchmark, two-dimensional statistics are
accumulated from a large number of Gaussian pseudorandom numbers,
which are generated according to a particular scheme that is
well-suited for parallel computation.  This problem is typical of many
``Monte-Carlo'' applications.  Since it requires almost no
communication, in some sense this benchmark provides an estimate of
the upper achievable limits for floating point performance on a
particular system.  Discussion on the parallel
implementation of this benchmark may be found in \cite{bailey}.

Results for the embarrassingly parallel benchmark are shown in Table
2.  Not all systems exhibit high rates on this problem.  This appears
to stem from the fact that this benchmark requires references to
several mathematical intrinsic functions, such as the Fortran routines
AINT, SQRT, and LOG, and evidently these functions are not highly
optimized on some systems.  

Results which have employed the reduced
precision table lookup scheme described in Section 2.1 
are unacceptable and not listed in the tables.
The SunMos-turbo operating system for the Paragon
allows both i860 processors on the node to be used for computation (in
regular SunMos and OSF the second processor is used purely for communication).

Intel Paragon results are due to S. Gupta and T. Phung of Intel.
CM-2, CM-200 and CM-5 results are due to J. Richardson of TMC.
SP-2 results are due to R. Agarwal, F. Gustavson and M. Zubair
of IBM.
KSR1 and KSR2 results are due to S. Breit (KSR), J. Singer (U. Houston), and
G. Shah (Georgia Tech).
VPP500 results are due to B. Elton of Fujitsu.
CS-2 results are due to J. Cownie and K. Pickard of Meiko and
L. Meadows of Portland Group.
SX-3 results are due to G.M. Sastri of NEC.
Power Challenge and Power Indigo results are due to J. Richardson of SGI.
Distributed workstation results are due to S. White of Emory
University \cite{white} except for the SGI results which are due to
D. Browning of the NAS System Development branch.  The ``Mixed-A''
computer system consisted of 16 Sun Sparc 1's, one Sun IPC, one Sun
Sparc2, 11 Sun SLC's, three IBM RS6000 model 550's, one IBM RS6000
model 530, and one NeXT machine.  The listed PVM results
used PVM 2.4 and Ethernet.

%%%%%%%%%%%%%%%%%%%
%%%%%% EP-A %%%%%%%%%
%%%%%%%%%%%%%%%%%%%
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|}
\hline
Computer System            &  Date    & No.   & Time   & Ratio to \\
                           &  Received& Proc. & (sec.) & Y-MP/1 \\
\hline
\hline
BBN TC2000                 & Dec 91   &   64  &   284.0 &  0.44 \\
\hline
Convex SPP1000		   & June 94   &    1  &   376.8 &  0.33\\
			   &          &    4  &    96.0 &  1.31\\
			   &          &    8  &    48.1 &  2.62\\
			   & Oct 94   &   16  &    24.3 &  5.19\\
\hline
Cray Y-MP                  & Aug 92   &    1  &   126.2 &  1.00 \\
                           &          &    8  &   15.9  &  7.95 \\
\hline 
Cray C-90                  &  Oct 94  &    1  &  46.31 &  2.72\\
                           &          &    4  &  11.59 & 10.89\\
                           &          &    8  &   5.84 & 21.60\\
                           &          &   16  &   2.95 & 42.81\\
\hline
Cray T3D                   & Oct 94   &   16  &  35.04 &  3.60 \\
			   &          &   32  &  17.52 &  7.20 \\
                           &          &   64  &   8.76 & 14.41 \\
                           &          &   128 &   4.38 & 28.81 \\
                           &          &   256 &   2.19 & 57.63 \\
                           &          &   512 &   1.09 & 115.78 \\
                           &          &   1024&   0.55 & 229.45 \\
\hline
Fujitsu VPP500             & Aug 94   &   1   &   44.25 & 2.85\\
                           &          &   4   &   11.24 & 11.21\\
                           &          &   8   &    5.67 & 22.22\\
                           &          &   16  &    2.87 & 43.97\\
                           &          &   32  &    1.46 & 86.44\\
                           &          &   64  &    0.75 & 167.92\\
\hline
IBM SP-2                   & Aug 94   & 8     & 44.26 & 2.85\\
                           &          & 16    & 22.15 & 5.70\\
                           &          & 32    & 11.08 & 11.38\\
                           &          & 64    &  5.53 & 22.82\\
\hline
Intel iPSC/860             & May 92   &   32  &   102.7  &  1.23 \\
                           &          &   64  &    51.4  &  2.46 \\
                           &          &  128  &    25.7  &  4.91 \\
\hline
Intel Paragon (OSF1.2)     & Mar 94   &  64   &  10.45 & 12.1\\
                           &          &  128  &   5.24 & 24.1\\
                           &          &  256  &   2.66 & 47.4\\
                           &          &  512  &   1.38 & 91.4\\
\hline
Intel Paragon (SunMos turbo)& Mar 94  &  64   &  5.27 & 23.9\\
                           &          &  128  &  2.76 & 45.7\\
                           &          &  256  &  1.46 & 86.4\\
\hline
Kendall Square KSR1        & Oct 93   & 16    & 101.9  &  1.2\\
                           &          & 32    & 51.4   & 2.5\\
                           &          & 64    & 26.0   & 4.9\\
                           &          & 128   & 12.8   & 9.9\\
\hline
Kendall Square KSR2        & Feb 94   & 32    & 24.8   &  5.1\\
			   & May 94   & 64    & 13.0   & 9.7 \\
\hline
Kyoto/Matsushita ADENART   & Feb 94   & 256   & 32.9   &  3.8\\
\hline
MasPar MP-1                & Aug 92   &  4K   &     248.0 &  0.51 \\
                           &          &  16K  &     69.3  &  1.82 \\
\hline
MasPar MP-2	           & Nov 92   &  16K  &     22.4  & 5.63 \\
\hline
\end{tabular}
\stepcounter{table}
\subcaption{Results of the Class A Embarrassingly Parallel (EP) Benchmark 
(cont'd)}
\end{center} \end{table}


%%\addtocounter{table}{-1}
\addtocounter{subtable}{-1}
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|}
\hline
Computer System            &  Date    & No.   & Time   & Ratio to \\
                           &  Received& Proc. & (sec.) & Y-MP/1 \\
\hline
\hline
Meiko CS-1                 & Aug 92   &  16   &     116.8 &  1.08 \\
\hline
Meiko CS-2                 & Oct 94   & 16    &     39.39 & 3.20 \\
                           &          & 32    &     20.45 & 6.16 \\
                           &          & 64    &     11.00 & 11.46 \\
                           &          & 96    &     7.84  & 16.07 \\
                           &          & 128   &     6.29  & 20.06 \\
\hline
nCUBE-2S		   & Mar 94   &   64  &   83.8   &  1.51\\
                           &          &   128 &   41.93  &  3.01\\
                           &          &   256 &   20.97  &  6.02\\
                           &          &   512 &   10.50  & 12.02\\
                           &          &  1024 &    5.25  & 24.03\\
\hline
NEC SX-3                   & Oct 94   &    1  &  21.27   & 5.93 \\
\hline
Silicon Graphics 	   & Oct 94   &    1  &  242.95  &  0.52\\
Power Challenge XL         &          &    4  &   61.44  &  2.05\\
                           &          &    8  &   30.77  &  4.10\\
                           &          &   16  &   15.48  &  8.15\\
\hline
Silicon Graphics Power Indigo& Oct 94   &    1  &   244.18 & 0.52 \\
\hline
Thinking Machines CM-2     & Oct 91   &   8K  &    126.6  &  1.00 \\
                           &          &  16K  &     63.9  &  1.97 \\
                           &          &  32K  &     33.7  &  3.74 \\
                           &          &  64K  &     18.8  &  6.71 \\
\hline
Thinking Machines CM-200   & Oct 91   &   8K  &     76.9  &  1.64 \\
                           &          &  16K  &     39.2  &  3.22 \\
                           &          &  32K  &     20.7  &  6.10 \\
                           &          &  64K  &     10.9  & 11.58 \\
\hline
Thinking Machines CM-5     & Nov 92   &   16  &     42.4  &  2.98 \\
                           &          &   32  &     21.5  &  5.88 \\
                           &          &   64  &     10.9  & 11.62 \\
                           &          &  128  &      5.4  & 23.49 \\
                           &          &  256  &      2.7  & 46.84 \\
                           &          &  512  &      1.4  & 90.47 \\
\hline
Thinking Machines CM-5E    & Feb 94   & 32    &     11.5  &  11.0\\
                           &          & 64    &     5.7   & 22.1\\
                           &          & 128   &     3.0   & 42.1\\
\hline
PVM Sparcs (Ethernet)      & Sep 93   &  16   &     1670.0 & 0.08 \\
\hline
PVM RS6000-550 (Ethernet) & Sep 93   &  4    &     890.0  & 0.14 \\
\hline
PVM Mixed-A (Ethernet)     & Sep 93   &  34   &     494.0  & 0.26 \\
\hline
PVM SGI 4D25 (Ethernet)    & Sep 93   &  4    &     2536.4 & 0.05 \\
\hline
Parasoft IBM (token)	   & Jan 94   & 9     &      589.0 & 0.2\\
\hline
\end{tabular}
\subcaption{(cont'd) Results of the Class A Embarrassingly Parallel (EP) Benchmark}
\end{center} \end{table}

%%%%%%%%%%%%%%%%%%%%%
%%%%%% EP-B %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|}
\hline
Computer System            &  Date    & No.   & Time   & Ratio to \\
                           &  Received& Proc. & (sec.) & C90/1 \\
\hline
\hline
Convex SPP1000		   & Aug 94   &   8   & 191.01 & 0.97 \\
                           &          &  16   &  96.55 & 1.92 \\
\hline
Cray C90                   & Oct 94   &   1   & 185.26 & 1.00\\
                           &          &   4   &  46.58 & 3.98\\
                           &          &   8   &  23.20 & 7.98\\
                           &          &   16  &  11.80 & 15.70\\
\hline
Cray T3D                   & Oct 94   &  16   & 140.13 & 1.32  \\
                           &          &  32   & 70.06 &  2.64 \\
                           &          &  64   & 35.03 &  5.29 \\
                           &          &  128  & 17.51 &  10.58\\
                           &          &  256  &  8.76 &  21.15\\
                           &          &  512  &  4.38 &  42.30\\
                           &          &  1024 &  2.19 &  84.59\\
\hline
Fujitsu VPP500             & Aug 94   &  1    & 176.64  & 1.05 \\
                           &          &  4    &  44.52  & 4.16 \\
                           &          &  8    &  22.36  & 8.29 \\
                           &          &  16   &  11.26  & 16.45 \\
                           &          &  32   &   5.68  & 32.62 \\
                           &          &  64   &   2.88  & 64.33 \\
\hline
IBM SP-2                   & Aug 94   &  8    & 153.90 & 1.20 \\
                           &          &  16   &  77.08 & 2.40 \\
                           &          &  32   &  38.28 & 4.84 \\
                           &          &  64   &  19.42 & 9.54 \\
                           & Oct 94   &  128  &   9.60 & 19.30 \\
\hline
Intel Paragon (OSF1.2)     & Mar 94   &  64   & 41.74 & 4.44 \\
                           &          &  128  & 20.86 & 8.88 \\
                           &          &  256  & 10.47 & 17.69 \\
                           &          &  512  &  5.26 & 35.22 \\
\hline
Intel Paragon (SunMos turbo)& Mar 94  &  64   & 21.18 & 8.75 \\
                           &          &  128  & 10.49 & 17.66 \\
                           &          &  256  &  5.41 & 34.24 \\
\hline
Kendall Square KSR2        & May 94   &  64   & 46.6   & 3.98 \\
\hline
Meiko CS-2                 & Aug 94   &  16   & 152.81 & 1.21 \\
                           &          &  32   &  77.20 & 2.40 \\
                           &          &  64   &  39.48 & 4.69 \\
                           &          &  96   &  26.84 & 6.90 \\
                           &          & 128   &  21.16 & 8.76 \\
\hline
nCUBE-2S		   & Mar 94   &  64   & 336.3  & 0.55\\
                           &          &  128  & 168.2  & 1.10 \\
                           &          &  256  &  84.1  & 2.20 \\
                           &          &  512  &  42.1  & 4.40 \\
                           &          &  1024 &  21.0  & 8.82 \\
\hline
NEC SX-3                   & Oct 94   &    1  &  81.58   & 2.27 \\
\hline
Silicon Graphics           & Oct 94   &  1    &  973.62 & 0.19 \\
Power Challenge XL         &          &  4    &  245.74 & 0.75 \\
                           &          &  8    &  122.98 & 1.51 \\
                           &          &  16   &   61.79 & 3.00 \\
\hline
Thinking Machines CM-5E    & Feb 94   &  32   &  46.9   & 3.95 \\
                           &          &  64   &  23.6   & 7.85 \\
                           &          &  128  &  11.6   & 15.97 \\
\hline
\end{tabular}
\subcaption{Results of the Class B Embarrassingly Parallel (EP) Benchmark}
\end{center} \end{table}

\subsection{Multigrid (MG) Benchmark}

The second kernel benchmark is a simplified multigrid kernel, which
solves a 3-D Poisson PDE.  This problem is simplified in the sense
that it has constant rather than variable coefficients as in a more
realistic application.  This code is a good test of both short and
long distance highly structured communication.  The Class B problem
uses the same size grid but a greater number of outer loop iterations.

Results for this benchmark are shown in Table 3.  
Intel Paragon results are due to J. Patterson of BCS and E. Kushner of Intel.  
CM-2 and CM-200 results are due to J.  Richardson at TMC.
RS6000-590 results are due to L.J. Shieh of IBM.
SP-1 and SP-2 results are due to R. Lawrence and C. Douglas of IBM.
KSR1 and KSR2 results are due to G. Montry of Southwest Software.
VPP500 results are due to J.C.H. Wang of Fujitsu.
CS-2 results are due to J. Cownie of Meiko.
SX-3 results are due to G.M. Sastri of NEC.
Distributed workstation results are due to S. White of Emory University
\cite{white} using PVM 2.4 and Ethernet except where noted otherwise.

%%%%%%%%%%%%%%%%%%%
%%%%%% MG-A %%%%%%%%%
%%%%%%%%%%%%%%%%%%%
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|}
\hline
Computer System          &  Date    & No.   & Time   & Ratio to \\
                         & Received & Proc. & (sec)  & Y-MP/1 \\
\hline
\hline
Convex SPP1000	         & Jun 94   &    1  &  208.0  &  0.11 \\
                         &          &    4  &   54.9  &  0.40 \\
                         &          &    8  &   30.9  &  0.72 \\
\hline
Cray Y-MP                & Aug 92   &    1  &   22.22 &  1.00 \\
                         &          &    8  &   2.96  &  7.51 \\
\hline
Cray  EL                 & Aug 92   &    1  &   89.19 &  0.25 \\
                         &          &    4  &   27.94 &  0.80 \\
                         &          &    8  &   22.30 &  0.95 \\
\hline
Cray C-90                &  Dec 93  &    1  &   8.15  &  2.7 \\
                         &          &    4  &   2.19  &  10.1 \\
                         &  Aug 92  &   16  &   0.96  & 23.14 \\
\hline
Cray T3D	         &  Oct 94  &   16  &  14.15  & 1.57 \\
	                 &          &   32  &   6.48  & 3.43 \\
	                 &          &   64  &   2.69  & 8.26 \\
	                 &          &  128  &   1.40  & 15.87 \\
			 &          &  256  &   0.76  & 29.24 \\
			 &          &  512  &   0.41  & 54.20 \\
			 &          &  1024 &   0.25  & 88.88 \\
\hline
Fujitsu VPP500	         & Aug 94   &  4    &    1.58 & 14.06 \\
                         &          &  8    &    0.86 & 25.84 \\
                         &          &  16   &    0.49 & 45.35 \\
                         &          &  32   &    0.33 & 67.33 \\
\hline
IBM RS6000-590          & Mar 94   &  1    &   41.78 & 0.53 \\
\hline
IBM SP-1                 & Mar 94   &  8    &   17.50 & 1.27 \\
                         &          & 16    &    9.49 & 2.34 \\
                         &          & 32    &    5.10 & 4.36 \\
                         &          & 64    &    2.89 & 7.69 \\
\hline
IBM SP-2                 & Aug 94   &  8    &   6.36  & 3.49 \\
                         &          &  16   &   3.32  & 6.69 \\
                         &          &  32   &   1.81  & 12.28 \\
                         &          &  64   &   1.00  & 22.22 \\
\hline
Intel iPSC/860           &  Aug 92  & 128   &   8.6   &  2.58 \\
\hline
Intel Paragon (OSF1.2)   & Mar 94   & 64    &   8.4   & 2.6\\
                         &          & 128   &   4.5   & 4.9\\
                         &          & 256   &   3.0   & 7.4\\
\hline
Intel Paragon (SunMos)   & Feb 94   & 64    &   9.76  &   2.3 \\
                         &          & 128   &   5.10  &   4.4 \\
                         &          & 256   &   3.48  &   6.4 \\
\hline
Kendall Square KSR1      & Feb 94   & 32    &   19.7  &   1.1 \\
                         &          & 64    &   10.3  &   2.2 \\
                         &          & 128   &   5.6   &  4.0 \\
\hline
Kendall Square KSR2      & Feb 94   & 32    &   10.3  &   2.20 \\
                         & May 94   & 64    &   5.7   &   3.90 \\
\hline
\end{tabular}
\stepcounter{table}
\subcaption{Results of the Class A Multigrid (MG) Benchmark (cont'd)}
\end{center} \end{table}

%
% table continued
%

\addtocounter{subtable}{-1}
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|}
\hline
Computer System            &  Date    & No.   & Time   & Ratio to \\
                           &  Received& Proc. & (sec.) & Y-MP/1 \\
\hline
\hline
Kyoto/Matsushita ADENART & Feb 94   & 256   &   21.4  &   1.0 \\
\hline
MasPar MP-1              & Aug 92   &   16K &   12.0  &  1.9 \\
\hline
MasPar MP-2              & Nov 92   &   16K &   4.36  &  5.1 \\
\hline
Meiko CS-1               & Aug 92   &   16  &   42.8  &  0.5 \\
\hline
Meiko CS-2               & Oct 94   &   16  &   7.60  & 2.93 \\
                         &          &   64  &   2.35  & 9.83 \\
                         &          &  128  &   1.43  & 15.54 \\
\hline
nCUBE-2S		 & Mar 94   &   64  &  37.6   &  0.6 \\
                         &          &  128  &  19.2   &  1.2 \\
                         &          &  512  &   5.3   &  4.2 \\
                         &          & 1024  &   2.8   &  7.9 \\
\hline
NEC SX-3                 & Oct 94   &   1   &   2.80  &  7.94 \\
\hline
Thinking Machines CM-2   & Dec 91   &   16K &   45.8  &  0.5 \\
                         &          &   32K &   26.0  &  0.9 \\
                         &          &   64K &   14.1  &  1.6 \\
\hline
Thinking Machines CM-200 & Dec 91   &   16K &   30.2  &  0.7 \\
                         &          &   32K &   17.2  &  1.3 \\
\hline
Thinking Machines CM-5   & Aug 93   &   32  &   19.5  &  1.1 \\
                         &          &   64  &   10.9  &  2.0 \\
                         &          &   128 &    6.1  &  3.6 \\
\hline
Thinking Machines CM-5E  & Feb 94   &   32  &   3.9   &  5.7 \\
                         &          &   64  &   2.3   &  9.9 \\
                         &          &   128 &   1.3   &  16.6\\
\hline
PVM RS6000-550 (Ethernet)& Sep 93  &    4  &  293.0  &  0.1 \\
\hline
PVM RS6000-560 (FDDI)   & Sep 93   &    4  &  184.0  &  0.1 \\
                         & Sep 93   &    8  &  110.4  &  0.2 \\
\hline
\end{tabular}
\subcaption{(cont'd) Results of the Class A Multigrid (MG) Benchmark}
\end{center} \end{table}
%%%%%%%%%%%%%%%%%%%
%%%%%% MG-B %%%%%%%%%
%%%%%%%%%%%%%%%%%%%
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|}
\hline
Computer System          &  Date    & No.   & Time   & Ratio to \\
                         & Received & Proc. & (sec)  & C90/1 \\
\hline
\hline
Cray C90                 & Dec 93   & 1     & 37.77  & 1.0\\
                         &          & 4     & 9.71   & 3.9\\
                         &          & 16    & 3.97   & 9.5\\
\hline
Cray T3D                 & Oct 94   & 16    & 66.58 & 0.57 \\ 
                         &          & 32    & 30.42 & 1.24 \\
                         &          & 64    & 12.56 & 3.01 \\
                         &          & 128   &  6.57 & 5.75 \\
                         &          & 256   &  3.60 & 10.49 \\
                         &          & 512   &  1.88 & 20.09 \\
                         &          & 1024  &  1.15 & 32.84 \\
\hline
Fujitsu VPP500           & Oct 94   & 4     & 7.53   & 5.02 \\
                         &          & 8     & 4.07   & 9.28 \\ 
                         &          & 16    & 2.35   & 16.07 \\
                         &          & 32    & 1.56   & 24.21 \\
\hline
IBM RS6000-590           & Mar 94   & 1     & 184.92 & 0.2\\
\hline
IBM SP-1                 & Mar 94   & 8     & 82.03  & 0.46 \\
                         &          & 16    & 44.57  & 0.85 \\
                         &          & 32    & 24.37  & 1.55 \\
                         &          & 64    & 13.86  & 2.73 \\
\hline
IBM SP-2                 & Aug 94   & 8     & 28.77  & 1.31 \\
                         &          & 16    & 15.09  & 2.50 \\
                         &          & 32    & 8.21   & 4.60 \\
                         &          & 64    & 4.53   & 8.34 \\
                         & Oct 94   & 128   & 2.63   & 14.36 \\
\hline
Intel Paragon (OSF1.2)   & Mar 94   & 64    & 39.8   & 0.9 \\
                         &          & 128   & 21.3   & 1.8\\
                         &          & 256   & 13.7   & 2.8\\
\hline
Intel Paragon (SunMos)   & Feb 94   & 64    & 43.02  &  0.9\\
                         &          & 128   & 24.15  &  1.6\\
                         &          & 256   & 16.74  &  2.3\\
\hline
Kendall Square KSR2      & May 94   & 64    & 26.1   & 1.45 \\
\hline
Meiko CS-2               & Oct 94   &   16  & 35.46  & 1.07 \\
                         &          &   64  & 10.76  & 3.51 \\
                         &          &  128  & 6.55   & 5.77 \\
\hline
NEC SX-3                 & Oct 94   &  1    & 13.16  & 2.87 \\
\hline
Thinking Machines CM-5E  & Feb 94   & 32    & 20.9   &  1.8\\
                         &          & 64    & 11.3   &  3.3\\
                         &          & 128   & 6.7    &  5.6\\
\hline
\end{tabular}
\subcaption{Results of the Class B Multigrid (MG) Benchmark}
\end{center} \end{table}

\subsection{Conjugate Gradient (CG) Benchmark}

In this benchmark, a conjugate gradient method is used to compute an
approximation to the smallest eigenvalue of a large, sparse, symmetric
positive definite matrix.  This kernel is typical of unstructured grid
computations in that it tests irregular long distance communication
and employs sparse matrix vector multiplication.

An unfortunate inconsistency has developed in the specification of
the Class A size CG benchmark.  The original benchmark description
(as written in RNR Technical Report RNR-91-002) specified 15 iterations,
however subsequent publications (specifically \cite{naspar})
specify 25 iterations.  For historical consistency we continue to report
timings for 15 iterations, and results we have received based on 25
iterations have been scaled by 15/25. (The
benchmark time scales linearly with number of iterations.)

Results which have circumvented the sparse matrix-vector multiplication
by retaining elements of the matrix construction, as described in Section 2.2,
are unacceptable and not listed in the tables.

The irregular communication requirement of this benchmark is evidently
a challenge for all systems.  Results are shown in Table 4.  CM-2
results are due to J.  Richardson of TMC.  Intel iPSC/860 and nCUBE-2
results are by B. Hendrickson, R. Leland, and S. Plimpton of Sandia
National Laboratory\cite{hend}.  
Paragon results are due to S. Gupta of Intel, R. van de Geijn of
U.T. Austin and John Lewis of BCS\cite{lewis}.  
Cray EL and C90 results are due to
M. Zagha of Carnegie Mellon University.  
VPP500 results are due to J. Wang of Fujitsu.
SP-1 results are due to D. Klepacki of IBM.
SP-2 results are due to D. Klepacki, B. Alpern and L. Carter of IBM.
KSR1 and KSR2 results are due to S. Breit and J. Middlecoff of KSR.
CS-2 results are due to D. Daniel of Meiko.
Power Challenge and Power Indigo results are due to F. Shakib of SGI.
Distributed workstation
results are due to S. White of Emory University \cite{white} using PVM
2.4 and Ethernet except where noted otherwise.

%%%%%%%%%%%%%%%%%%%
%%%%%% CG-A %%%%%%%%%
%%%%%%%%%%%%%%%%%%%
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|}
\hline
Computer System          &  Date    & No.   & Time   & Ratio to \\
                         & Received & Proc. & (sec.) & Y-MP/1 \\
\hline
\hline
BBN TC2000               & Dec 91   &   40  &   51.4 &  0.23 \\
\hline
Convex SPP1000           & Jun 94   &    1  & 202.9  & 0.06 \\
                         &          &    4  &  49.7  & 0.24 \\
                         &          &    8  &  23.9  & 0.50 \\
                         & Oct 94   &   16  &  12.0  & 0.99 \\
\hline
Cray Y-MP                & Aug 92   &    1  &  11.92 &  1.00 \\
                         &          &    8  &   2.38 &  5.01 \\
\hline
Cray EL                  & Sep 93   &    1  & 45.24  & 0.26\\  
                         &          &    4  & 14.29  & 0.83\\
                         &          &    8  & 10.14  & 1.18\\
\hline
Cray C-90                & Sep 93   &    1  & 3.55   & 3.36\\ 
                         &          &    4  & 0.96   & 12.42\\
                         &          &   16  & 0.34   & 35.06\\
\hline
Cray T3D	         & Jul 94   &   16  & 14.98  & 0.80 \\
			 &          &   32  &  7.46  & 1.60 \\
                         &          &   64  &  4.20  & 2.84 \\
                         &          &   128 &  2.23  & 5.35 \\
                         &          &   256 &  1.30  & 9.17 \\
                         & Oct 94   &   512 &  0.81  & 14.72 \\
                         &          &   1024&  0.58  & 20.55\\
\hline
Fujitsu VPP500           & Mar 94   &  1    &  5.68  & 2.10 \\
                         &          &  2    &  3.06  & 3.90 \\
                         &          &  4    &  1.72  & 6.93 \\
                         &          &  8    &  1.04  & 11.46 \\
                         & Aug 94   & 16    &  0.80  & 14.90 \\
\hline
IBM SP-1                 & Feb 94   &   8   & 21.37  & 0.6\\
                         &          &   16  & 12.82  & 0.9\\
                         &          &   32  & 7.98   & 1.5\\
                         &          &   64  & 4.72   & 2.5\\
\hline
IBM SP-2                 & Aug 94   &   8   & 4.91   &  2.43 \\
                         &          &   16  & 3.15   &  3.78 \\
                         &          &   32  & 2.45   &  4.86 \\
                         &          &   64  & 1.81   &  6.58 \\
\hline
Intel iPSC/860           & Sep 93   &   128 &   7.0  &  1.71 \\
\hline
Intel Paragon (OSF1.2)   & Mar 94   &    64 &  4.10  &  2.9 \\
                         &          &   128 &  3.30  &  3.6 \\
                         &          &   256 &  2.83  &  4.2 \\
\hline
Intel Paragon (SunMos) 	 & Nov 93   &    64 &  12.6  &  1.0 \\
\hline
Kendall Square KSR1      & Feb 94   &    32 & 19.0   & 0.6\\
                         &          &    64 & 13.4   & 0.9\\
\hline
Kendall Square KSR2      & Feb 94   &    32 & 9.8    & 1.2\\
                         & May 94   &    64 & 6.1    & 1.95 \\
\hline
\end{tabular}
\stepcounter{table}
\subcaption{Results of the Class A Conjugate Gradient (CG) Benchmark (cont'd)}
\end{center} \end{table}

%
% table continued
%
\addtocounter{subtable}{-1}
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|}
\hline
Computer System            &  Date    & No.   & Time   & Ratio to \\
                           &  Received& Proc. & (sec.) & Y-MP/1 \\
\hline
\hline
Kyoto/Matsushita ADENART & Feb 94   &  256 &   10.8  & 1.1 \\
\hline
MasPar MP-1              & Aug 92   &   4K &   64.5  &  0.18 \\
                         &          &  16K &   14.6  &  0.82 \\
\hline
MasPar MP-2              & Nov 92   &  16K &   11.0  &  1.08 \\
\hline
Meiko CS-1               & Aug 92   &   16 &   67.5  &  0.18 \\
\hline
Meiko CS-2               & Oct 94   &   16 &   7.18  &  1.66 \\
                         &          &   32 &   5.60  &  2.10 \\
\hline
nCUBE-2S                 & Mar 94   &   64 &   29.6  &  0.4 \\
                         &          &  128 &   16.9  &  0.7 \\
                         &          &  256 &    9.6  &  1.3  \\
                         &          &  512 &    6.2  &  1.9  \\
                         &          & 1024 &    4.1  &  2.9  \\
\hline
Silicon Graphics         & Oct 94   &   1  &   39.0  & 0.31\\
Power Challenge XL       &          &   2  &   16.9  & 0.71 \\
                         &          &   4  &    7.2  & 1.66 \\
                         &          &   8  &    4.5  & 2.65 \\
                         &          &  16  &    3.5  & 3.41 \\
\hline
Silicon Graphics Power Indigo   & Oct 94   &   1  &  52.27  & 0.22\\
\hline
Thinking Machines CM-2   & Mar 92   &    8K &   25.6 &  0.47 \\
                         &          &   16K &   14.1 &  0.85 \\
                         &          &   32K &   8.8  &  1.35 \\
\hline
Thinking Machines CM-200 & Mar 92   &   8K &   15.0  &  0.79 \\
\hline
Thinking Machines CM-5   & Aug 93   &   32 &   20.7  &  0.58 \\
                         &          &   64 &   10.6  &  1.12 \\
                         &          &  128 &   6.2   &  1.92 \\
\hline
PVM RS6000-550 (Ethernet)& Sep 93  &    4  & 203.2  &  0.06 \\
\hline
PVM RS6000-560 (FDDI)   & Sep 93   &    4  &  81.5  &  0.15 \\
\hline
Parasoft IBM (token)     & Jan 94   &    9  &  277   &   0.04 \\
\hline
\end{tabular}
\subcaption{(cont'd) Results of the Class A Conjugate Gradient (CG) Benchmark}
\end{center} \end{table}

%%%%%%%%%%%%%%%%%%%
%%%%%% CG-B %%%%%%%
%%%%%%%%%%%%%%%%%%%
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|}
\hline
Computer System          &  Date    & No.   & Time   & Ratio to \\
                         & Received & Proc. & (sec.) & C90/1 \\
\hline
\hline
Cray C90                 & Dec 93   & 1     & 122.90 & 1.00 \\
                         &          & 4     & 33.19  & 3.7 \\
                         &          & 16    & 10.61  & 11.6 \\
\hline
Cray T3D                 & Jul 94   & 16    & 582.05  & 0.21 \\
                         &          & 32    & 298.62  & 0.41 \\
                         &          & 64    & 166.57  & 0.74 \\
                         &          & 128   &  85.51  & 1.44 \\
                         &          & 256   &  50.18  & 2.45 \\
                         & Oct 94   & 512   &  27.34  & 4.50 \\
                         &          & 1024  &  16.58  & 7.41 \\
\hline
Fujitsu VPP500           & Apr 94   & 2     & 104.51  & 1.18 \\
                         &          & 4     &  55.40  & 2.22 \\
                         &          & 8     &  31.80  & 3.86 \\
                         & Aug 94   & 15    &  20.85  & 5.89 \\
                         &          & 30    &  15.21  & 8.08 \\
\hline
IBM RS6000-590           & Mar 94   & 1     & $429.0^*$ & $0.3^*$ \\
\hline
IBM SP-1                 & Mar 94   & 16    & 638.2  & 0.2 \\
                         &          & 32    & 362.9  & 0.3 \\
                         &          & 64    & 193.4  & 0.6 \\
\hline
IBM SP-2                 & Aug 94   & 8     & 165.70 & 0.74 \\
                         &          & 16    &  93.72 & 1.31 \\
                         &          & 32    &  64.21 & 1.91 \\
                         &          & 64    &  42.68 & 2.88 \\
                         & Oct 94   & 128   &  26.79 & 4.59 \\
\hline
Intel Paragon (OSF1.2)   & Mar 94   & 128    & 132.5  &  0.9 \\
                         & Jul 94   & 256    & 70.0   &  1.76 \\
                         &          & 512    & 47.6   &  2.58 \\
\hline
Kendall Square KSR2      & May 94   & 64    & 182.0   &  0.68 \\
\hline
Meiko CS-2               & Oct 94   &   16  &  248.30 & 0.49 \\
                         &          &   32  &  156.50 & 0.78 \\
\hline
Thinking Machines CM-5E  & Feb 94   & 32    & $449.0^*$  &  $0.3^*$ \\
                         &          & 64    & $199.0^*$  &  $0.6^*$ \\
                         &          & 128   & $92.0^*$   & $1.3^*$ \\
\hline
\end{tabular}
\subcaption{Results of the Class B Conjugate Gradient (CG) Benchmark
($^*$ indicates result used matrix construction to circumvent sparse
matrix-vector multiplication)}
\end{center} \end{table}

\subsection{3-D FFT PDE (FT) Benchmark}

In this benchmark a 3-D partial differential equation is solved using
FFTs.  This kernel performs the essence of many ``spectral'' codes.
It is a good test of long-distance communication performance.
Discussion on the parallel implementation of this benchmark may be
found in \cite{bailey}.

The rules of the NAS Parallel Benchmarks specify that assembly-coded,
library routines may be used to perform matrix multiplication and
one-dimensional, two-dimensional or three-dimensional FFTs.  Thus this
benchmark is somewhat unique in that computational library routines
may be legally employed.  

Results are shown in Table 5.  
Intel Paragon results are due to E. Kushner and T. Phung of Intel.  
VPP500 results are due to S. Zarantonello of Fujitsu.
CM-2 and CM-200 results are due to J. Richardson of TMC.  
RS6000-590, SP-1 and SP-2 results are due to 
F. Gustavson, M. Zubair and R. Agarwal of IBM.
KSR1 and KSR2 results are due to N. Camp of KSR.
MP-1 and MP-2 results are due to J. Fier of MasPar.
CS-2 results are due D. Daniel of Meiko.
SX-3 results are due to G.M. Sastri of NEC.
Power Challenge and Power Indigo results are due to J. Fier of SGI.

%%%%%%%%%%%%%%%%%%%
%%%%%% FT-A %%%%%%%%%
%%%%%%%%%%%%%%%%%%%
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|}
\hline
Computer System          &  Date    & No.   & Time   & Ratio to \\
                         & Received & Proc. & (sec.) & Y-MP/1 \\
\hline
\hline
Convex SPP1000	         & Aug 94   &  1    & $178.57^*$& 0.16 \\
                         &          &  4    & $46.78^*$ & 0.62 \\
                         &          &  8    & $25.54^*$ & 1.13 \\
\hline
Cray Y-MP                & Aug 92   & 1     & $28.77^*$ &  1.00 \\
                         &          &   8   &  $4.19^*$ &  6.87 \\
\hline
Cray EL                  & May 93   &   1   & $105.1^*$ &  0.27 \\
                         &          &   4   &  $27.9^*$ &  1.03 \\
                         &          &   8   &  $18.5^*$ &  1.56 \\
\hline
Cray C-90                & Aug 92   &   1   & $10.28^*$ &  2.80 \\
                         &          &   4   &  $2.58^*$ & 11.20 \\
                         &          &  16   &  $0.91^*$ & 31.60 \\
\hline
Cray T3D                 & Oct 94   &  16   & $11.86^*$ & 2.43 \\
                         &          &  32   & $6.00^*$  & 4.80 \\
                         &          &  64   & $3.07^*$  & 9.37 \\
                         & Jul 94   &  128  & $1.57^*$  & 18.32 \\
                         &          &  256  & $0.80^*$  & 35.96 \\
                         & Oct 94   &  512  & $0.54^*$  & 53.28 \\
                         &          &  1024 & $0.32^*$  & 89.91 \\
\hline
Fujitsu VPP500		 & Aug 94   &   4   & $2.93$ & 9.82 \\
                         &          &   8   & $1.45$ & 19.81 \\
                         &          &   16  & $0.75$ & 38.51 \\
                         &          &   32  & $0.40$ & 72.47 \\
                         &          &   64  & $0.24$ & 121.91 \\
\hline
IBM RS6000-590          & Feb 94   &  1    & $61.01^*$ & 0.5 \\
\hline
IBM SP-1                 & Feb 94   &  8    & $43.68^*$ & 0.7 \\
                         &          &  16   & $22.86^*$ & 1.3 \\
                         &          &  32   & $12.08^*$ & 2.4 \\
                         &          &  64   & $6.46^*$  & 4.5 \\
\hline
IBM SP-2                 & Aug 94   &  8    & $14.59^*$ & 1.97 \\
                         &          &  16   &  $7.79^*$ & 3.70 \\
                         &          &  32   &  $4.87^*$ & 5.91 \\
                         &          &  64   &  $2.42^*$ & 11.89 \\
\hline
Intel iPSC/860           & Dec 91   &  64   &  $20.9^*$ &  1.37 \\
                         & Apr 92   & 128   &   $9.7^*$ &  2.96 \\
\hline
Intel Paragon (OSF1.2)   & Mar 94   &  64   &   $9.1^*$ & 3.2 \\
                         &          & 128   &   $4.9^*$ & 5.9 \\
                         &          & 256   &   $3.6^*$ & 8.0 \\
\hline
Intel Paragon (SunMos)   & Mar 94   & 64    & $7.2^*$  &  4.0 \\
                         &          & 128   & $3.9^*$  &  7.4 \\
                         &          & 256   & $3.0^*$  &  9.7 \\
\hline
Kendall Square KSR1      & Feb 94   & 32    & $16.2^*$  &   1.8 \\
                         &          & 64    & $9.2^*$   &  3.1 \\
\hline
Kendall Square KSR2      & Feb 94   & 32    & $9.0^*$   &  3.2 \\
                         & May 94   & 64    & $6.5^*$   &  4.43 \\
\hline   
\end{tabular}
\stepcounter{table}
\subcaption{Results of the Class A 3-D FFT PDE (FT) Benchmark 
(cont'd) ($^*$ indicates library result).}
\end{center} \end{table}


%%%%%%%%%%%%%%%%%%%
\addtocounter{subtable}{-1}
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|}
\hline
Computer System            &  Date    & No.   & Time   & Ratio to \\
                           &  Received& Proc. & (sec.) & Y-MP/1 \\
\hline
\hline
Kyoto/Matsushita ADENART & Feb 94   & 256   & 72.7      & 0.4 \\
\hline   
MasPar MP-1              & Aug 92   &  16K  &  $18.3^*$ &  1.57 \\
\hline
MasPar MP-2	         & Nov 92   &   16K  & $8.0^*$  &  3.60\\
\hline   
Meiko CS-1               & Aug 92   &  16   & $170.0^*$ &  0.17 \\
\hline   
Meiko CS-2               & Oct 94   &  16   & 12.67    &  2.27 \\
                         &          &  32   &  7.17    & 4.01 \\
                         &          &  64   &  4.53    & 6.35 \\
\hline   
nCUBE-2S		 & Mar 94   &  64   & $62.8^*$  &  0.5 \\
                         &          & 128   & $32.9^*$  &  0.9 \\
                         &          & 256   & $16.0^*$  &  1.8 \\
                         &          & 512   &  $8.4^*$  &  3.4 \\
                         &          &1024   &  $4.1^*$  &  7.0 \\
\hline   
NEC SX-3                 & Oct 94   & 1     & 2.79$^*$  &  10.31 \\
\hline   
Silicon Graphics         & Oct 94   &  1    & $61.17^*$ &  0.47 \\
Power Challenge XL       &          &  2    & $35.53^*$ &  0.81 \\
                         &          &  4    & $19.98^*$ &  1.44 \\
                         &          &  8    & $12.57^*$ &  2.29 \\
                         &          &  16   & $11.18^*$ &  2.57 \\
\hline   
Thinking Machines CM-2   & Dec 91   & 16K   &  $37.0^*$ &  0.78 \\
                         &          & 32K   &  $18.2^*$ &  1.58 \\
                         &          & 64K   &  $11.4^*$ &  2.52 \\
\hline
Thinking Machines CM-200 & Dec 91   &  8K   &  $45.6^*$ &  0.63 \\
\hline
Thinking Machines CM-5   & Aug 93   &  32   & $14.9^*$ &  1.93 \\
                         &          &  64   &  $7.9^*$ &  3.64 \\
                         &          &  128  &  $6.6^*$ &  4.36 \\
\hline   
Thinking Machines CM-5E  & Feb 94   & 32    & $7.4^*$  &   3.9 \\
                         &          & 64    & $3.9^*$  &   7.4 \\
                         &          & 128   & $2.9^*$  &   9.9 \\
\hline   
\end{tabular}
\subcaption{(cont'd) Results of the Class A 3-D FFT PDE (FT) Benchmark 
($^*$ indicates library result).}
\end{center} \end{table}
%%%%%%%%%%%%%%%%%%%
%%%%%% FT-B %%%%%%%%%
%%%%%%%%%%%%%%%%%%%
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|}
\hline
Computer System          &  Date    & No.   & Time   & Ratio to \\
                         & Received & Proc. & (sec.) & C90/1 \\
\hline
\hline
Convex SPP1000           & Aug 94   & 8     & $375.43^*$ & 0.34 \\
\hline
Cray C90                 & Dec 93   & 1     & $127.44^*$ &  1.00 \\
                         &          & 2     & $63.74^*$  & 2.0 \\
                         &          & 16    & $8.43^*$   & 15.1 \\
\hline
Cray T3D                 & Oct 94   & 64    & $40.80^*$  & 3.12 \\
                         &          & 128   & $20.96^*$  & 6.08 \\
                         & July 94  & 256   & $10.89^*$  & 11.70 \\
                         & Oct 94   & 512   &  $6.73^*$  & 18.94 \\
                         &          & 1024  &  $3.76^*$  & 33.89 \\
\hline
Fujitsu VPP500           & Aug 94   & 16    &  $7.95$ & 16.03 \\
                         &          & 32    &  $4.07$ & 31.33 \\
                         &          & 64    &  $2.18$ & 58.54 \\
\hline
IBM RS6000-590           & Mar 94   & 1     & $856.3^*$ & 0.1  \\
\hline
IBM SP-1                 & Mar 94   & 16    & $286.5^*$ & 0.4 \\
                         &          & 32    & $143.2^*$ & 0.9 \\
                         &          & 64    & $74.5^*$  & 1.7 \\
\hline
IBM SP-2                 & Aug 94   & 16    & $96.02^*$ & 1.33 \\
                         &          & 32    & $52.98^*$ & 2.40 \\
                         &          & 64    & $28.50^*$ & 4.47 \\
                         & Oct 94   & 128   & $14.57^*$ & 8.75 \\
\hline
Kendall Square KSR2      & May 94   & 64    & $124.0^*$ & 1.03 \\
\hline
Intel Paragon (OSF1.2)   & Mar 94   & 128   & $56.5^*$ & 2.3\\ 
                         &          & 256   & $30.6^*$ & 4.2\\
\hline
Intel Paragon (SunMos)   & Feb 94   & 256   & $25.1^*$ &  5.1 \\
\hline
Meiko CS-2               & Oct 94   &  32   & 82.71    &  1.54 \\
                         &          &  64   & 48.04    &  2.65 \\
\hline
NEC SX-3                 & Oct 94   &   1   & 37.52$^*$ & 3.40 \\
\hline
Silicon Graphics         & Oct 94   &   1   & $761.67^*$ & 0.17 \\
Power Challenge XL       &          &   2   & $414.52^*$ & 0.31 \\
                         &          &   4   & $223.97^*$ & 0.57 \\
                         &          &   8   & $130.15^*$ & 0.98 \\
                         &          &   16  & $110.37^*$ & 1.15 \\
\hline
Thinking Machines CM-5E  & Feb 94   & 32    & $89.0^*$  &  1.4 \\
                         &          & 64    & $46.0^*$  &  2.8 \\
                         &          & 128   & $34.0^*$  &  3.7 \\
\hline   
\end{tabular}
\subcaption{Results of the Class B 3-D FFT PDE (FT) Benchmark ($^*$ indicates library
result).}
\end{center} \end{table}

\subsection{Integer Sort (IS) Benchmark}

This benchmark tests a sorting operation that is important in
``particle method'' codes.  This type of application is similar to
``particle in cell'' applications of physics, wherein particles are
assigned to cells and may drift out.  The sorting operation is used to
reassign particles to the appropriate cells.  This benchmark tests
both integer computation speed and communication performance.
For discussion on general parallel algorithms for this 
benchmark see \cite{dagum}.

This problem is unique in that floating point arithmetic is not
involved.  Significant data communication, however, is required.
Results are shown in Table 6.  
Intel Paragon results are due to to S. Gupta and B. Greer of Intel.  
CM-2, CM-200 and MasPar results use a library sorting routine.
Cray Y-MP results are due to CRI.  Cray C-90 and EL results are
due to M. Zagha of Carnegie Mellon University using a radix sort
optimized for interleaved memories \cite{zagha}.
VPP500 results are due to B. Elton of Fujitsu.
RS6000-590, SP-1 and SP-2 results are due 
to F. Gustavson, M. Zubair and R. Agarwal
of IBM.
KSR1 and KSR2 results are due to C. Nowacki of KSR.


%%%%%%%%%%%%%%%%%%%
%%%%%% IS-A %%%%%%%%%
%%%%%%%%%%%%%%%%%%%
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|}
\hline
Computer System          &  Date    & No.   &   Time   & Ratio to \\
                         & Received & Proc. &   (sec.) & Y-MP/1 \\
\hline
\hline
Convex SPP1000           & Jun 94   &   1   &    76.8  & 0.15 \\
                         &          &   4   &    24.5  & 0.47 \\
                         &          &   8   &    14.6  & 0.78 \\
\hline
Cray Y-MP                & Aug 92   &   1   &    11.46 &  1.00  \\
                         &          &   8   &    1.85  &  6.19  \\
\hline
Cray EL                  & Sep 93   &   1   &    43.76  &  0.26\\
                         &          &   4   &    12.99  &  0.88\\
                         &          &   8   &    8.45   &  1.35\\
\hline
Cray C-90                & Sep 93   &  1    &     3.33  & 3.44\\
                         &          &  4    &     0.85  & 13.46\\ 
                         &          &  16   &     0.27  & 42.38\\
\hline
Cray T3D                 & Oct 94   & 16    &   11.86   & 0.97 \\
                         &          & 32    &    5.87   & 1.95 \\
                         &          & 64    &    2.89   & 3.97 \\
                         &          & 128   &    1.49   & 7.69 \\
                         &          & 256   &    0.81   & 14.15 \\
                         &          & 512   &    0.54   & 21.22 \\
                         &          & 1024  &    0.44   & 26.05 \\
\hline
Fujitsu VPP500           & Apr 94   & 1     &    2.189  & 5.24 \\
                         &          & 2     &    1.574  & 7.28 \\
                         &          & 4     &    1.098  & 10.44 \\
                         &          & 8     &    0.917  & 12.50 \\
\hline
IBM RS6000-590          & Feb 94   & 1     &   21.73   & 0.5 \\
\hline
IBM SP-1                 & Feb 94   & 8     &   16.81   & 0.7 \\
                         &          & 16    &   8.85    & 1.3 \\
                         &          & 32    &   5.04    & 2.3 \\
                         &          & 64    &   3.06    & 3.7 \\
\hline
IBM SP-2                 & Aug 94   & 8     &   5.00    & 2.29 \\
                         &          & 16    &   2.79    & 4.11 \\
                         &          & 32    &   1.77    & 6.47 \\
                         &          & 64    &   0.93    & 12.32 \\
\hline
Intel iPSC/860           & May 92   &  32   &     25.7  & 0.45   \\
                         &          &  64   &     17.3  & 0.66   \\
                         &          & 128   &     13.6  & 0.84   \\
\hline
Intel Paragon (OSF1.2)   & Mar 94   &  32   &     7.81  & 1.5 \\
                         &          &  64   &     4.34  & 2.6 \\
                         &          &  128  &     2.41  & 4.8 \\
\hline
Intel Paragon (SunMos)   & Mar 94   & 32    &     5.48  & 2.1 \\
	                 &          & 64    &     3.77  & 3.0 \\
\hline
Kendall Square KSR1      & Feb 94   & 32    &     10.8  &   1.1 \\
                         &          & 64    &     6.6   &  1.7 \\
\hline
Kendall Square KSR2      & Feb 94   & 32    &     7.0   &  1.6 \\
                         & May 94   & 64    &     3.9   &  2.94 \\
\hline
\end{tabular}
\stepcounter{table}
\subcaption{Results of the Class A Integer Sort (IS) Benchmark (cont'd)
($^*$ indicates library result).}
\end{center} \end{table}

\addtocounter{subtable}{-1}
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|}
\hline
Computer System            &  Date    & No.   & Time   & Ratio to \\
                           &  Received& Proc. & (sec.) & Y-MP/1 \\
\hline
\hline
Kyoto/Matsushita ADENART & Feb 94   & 256   &     46.6  &   0.3 \\
\hline
MasPar MP-1              & Jan 93   &  16K  &  $11.5^*$ &  1.00 \\
\hline
MasPar MP-2	         & Jan 93   &  16K  &   $7.7^*$ &  1.49 \\
\hline
Meiko CS-1               & Aug 92   &  16   &     62.7  &  0.18 \\
\hline
nCUBE-2S		 & Mar 94   &   64  &   23.2    &  0.5 \\
                         &          &  128  &   12.0    &  1.0\\
                         &          &  256  &    6.1    &  1.9\\
                         &          &  512  &    3.2    &  3.6\\
                         &          & 1024  &    1.7    &  6.8\\
\hline
Thinking Machines CM-2   & Dec 91   & 16K   &   $35.8^*$ &  0.32 \\
                         &          & 32K   &   $21.0^*$ &  0.55 \\
                         &          & 64K   &   $14.9^*$ &  0.77 \\
\hline
Thinking Machines CM-200 & Dec 91   & 64K   &    $5.7^*$&  2.01\\
\hline
Thinking Machines CM-5   & Aug 93   &  32   &     43.1  &  0.27  \\
                         &          &  64   &     24.2  &  0.47  \\
                         &          &  128  &     12.0  &  0.96  \\
\hline
Thinking Machines CM-5E  & Feb 94   & 32    &     6.3   &  1.8 \\
                         &          & 64    &     3.1   &  3.7  \\
                         &          & 128   &     1.66  &  6.9  \\
\hline
\end{tabular}
\subcaption{(cont'd) Results of the Class A Integer Sort (IS) Benchmark 
($^*$ indicates library result).}
\end{center} \end{table}
%%%%%%%%%%%%%%%%%%%
%%%%%% IS-B %%%%%%%%%
%%%%%%%%%%%%%%%%%%%
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|}
\hline
Computer System          &  Date    & No.   &   Time   & Ratio to \\
                         & Received & Proc. &   (sec.) & C90/1 \\
\hline
\hline
Cray C90                 & Dec 93   & 1     &   12.92  &  1.00 \\
                         &          & 4     &   3.30   &  3.9 \\
                         &          & 16    &   0.98   & 13.7 \\
\hline
Cray T3D                 & Oct 94   & 32    &   25.46  & 0.51 \\
                         &          & 64    &   12.88  & 1.00 \\
                         &          & 128   &    6.57  & 1.97 \\
                         &          & 256   &    3.27  & 3.95 \\
                         &          & 512   &    1.94  & 6.66 \\
                         &          & 1024  &    1.22  & 10.59 \\
\hline
Fujitsu VPP500           & Apr 94   & 4     &   3.70  & 3.49 \\
                         &          & 8     &   3.03  & 4.26 \\
\hline
IBM RS6000-590           & Mar 94   & 1     &   91.6  & 0.1 \\
\hline
IBM SP-1                 & Mar 94   & 16    &   37.3  & 0.3 \\
                         &          & 32    &   20.1  & 0.6 \\
                         &          & 64    &   11.2  & 1.2 \\
\hline
IBM SP-2                 & Aug 94   & 8     &   19.98 & 0.65 \\
                         &          & 16    &   11.04 & 1.17 \\
                         &          & 32    &    6.88 & 1.88 \\
                         &          & 64    &    3.55 & 3.64 \\
                         & Oct 94   & 128   &    1.99 & 6.49 \\
\hline
Intel Paragon (OSF1.2)   & Mar 94   & 64    &   17.33 & 0.7  \\
                         &          & 128   &    9.52 & 1.4\\
                         &          & 256   &    5.94 & 2.2\\
                         &          & 512   &    4.69 & 2.8\\
\hline
Intel Paragon (SunMos)   & Mar 94   & 64    &   11.98 & 1.1 \\
                         &          & 128   &    7.22 & 1.8\\
\hline
Kendall Square KSR2      & May 94   & 64    &   20.3  & 0.64 \\
\hline
nCUBE-2S		 & Mar 94   &  128  &   47.5  & 0.3 \\
                         &          &  512  &   12.5  & 1.0 \\
                         &          & 1024  &    6.5  & 2.0 \\
\hline
Thinking Machines CM-5E  & Feb 94   & 32    &   32.0   &  0.4 \\
                         &          & 64    &   16.4   &  0.8 \\
                         &          & 128   &   8.4    & 1.5 \\
\hline
\end{tabular}
\subcaption{Results of the Class B Integer Sort (IS) Benchmark}
\end{center} \end{table}


\section{Simulated CFD Application Benchmarks}

The three simulated CFD application benchmarks are intended to
accurately represent the principal computational and data movement
requirements of modern CFD applications.

The first of these is the called the lower-upper diagonal (LU)
benchmark.  It does not perform a LU factorization but instead employs
a symmetric successive over-relaxation (SSOR) numerical scheme to
solve a regular-sparse, block $(5 \times 5)$ lower and upper
triangular system.  This problem represents the computations
associated with a newer class of implicit CFD algorithms, typified at
NASA Ames by the code ``INS3D-LU''.  This problem exhibits a somewhat
limited amount of parallelism compared to the next two.
Discussion of the serial algorithm underlying this benchmark may be found
in \cite{yoon}.  Discussion of the parallel algorithms may be found in
\cite{bars}.

The second simulated CFD application is called the scalar
pentadiagonal (SP) benchmark.  In this benchmark, multiple independent
systems of non-diagonally dominant, scalar pentadiagonal equations are
solved.  The third simulated CFD application is called the block
tridiagonal (BT) benchmark.  In this benchmark, multiple independent
systems of non-diagonally dominant, block tridiagonal equations with a
$5 \times 5$ block size are solved.

SP and BT are representative of computations associated with the
implicit operators of CFD codes such as ``ARC3D'' at NASA Ames.  SP
and BT are similar in many respects, but there is a fundamental
difference with respect to the communication to computation ratio.
Discussion of the serial algorithm underlying this benchmark may be found
in \cite{pulliam}.

Performance figures for the three simulated CFD applications are shown
in Tables 7, 8 and 9.  Timings are cited as complete run times, in
seconds, as with the other benchmarks.  A complete solution of the LU
benchmark requires 250 iterations.  For the SP benchmark, 400
iterations are required.  For the BT benchmark, 200 iterations are
required.

For LU, credits are as follows: 
iPSC/860 and CM-2 results are due to
S. Weeratunga, R. Fatoohi, E. Barszcz and V. Venkatakrishnan of NAS;
VPP500 results are due to C. Chen of Fujitsu;
CM-5 results are due to J. Richardson and D. Sandee of TMC; 
MP-1 and MP-2 results are due to J. McDonald of MasPar; 
Intel Paragon results are due to T. Phung and E. Kushner of Intel; 
KSR1 and KSR2 results are due to S. Breit of KSR;
RS600-590 results are due to L.E. Hannon of IBM;
SP-1 and SP-2 results are due to V. Naik of IBM;
nCUBE-2S results are due to E. Schulman of nCUBE;
Power Challenge and Power Indigo results are due to J. McDonald of SGI.

For SP, credits are as follows: 
CM-2 results employ a library scalar pentadiagonal solver;
CM-5 results are due to J. Richardson and D. Sandee of TMC; iPSC/860
results are due to J. Patterson of BCS; 
Paragon results are due to T. Phung of Intel for tranpose algorithm,
and R. van de Wijngaar of MCAT for multipartition method; 
MP-1 and MP-2 results are due to J. McDonald of
MasPar; KSR1 and KSR2 results are due to S. Breit of KSR and G. Shah of 
Georgia Tech;
RS600-590 results are due to L.J. Shieh of IBM;
SP-1 and SP-2 results are due to V. Naik of IBM;
VPP500 results are due to S. Gavali of Fujitsu;
SX-3 results are due to G.M. Sastri of NEC;
nCUBE-2S results are due to E. Schulman of nCUBE;  
Power Challenge and Power Indigo results are due to J. Bannning of SGI.

For BT, credits are as follows: 
CM-2 and CM-200 results employ a library block tridiagonal solver;
CM-5 results are due to J. Richardson and D. Sandee of TMC; 
iPSC/860 results are due to J. Patterson of BCS;
Paragon results are due to T. Phung of Intel; MP-1 and MP-2 results
are due to J. McDonald of MasPar; 
KSR1 and KSR2 results are due to S. Breit of KSR;
RS600-590 results are due to L.J. Shieh of IBM;
SP-1 and SP-2 results are due to V. Naik of IBM;
VPP500 results are due to H. Lai of Fujitsu and staff of Fujitsu Limited;
CS-2 results are due G. Montry of Southwest Software.
SX-3 results are due to G.M. Sastri of NEC;
nCUBE-2S results are due to E. Schulman of nCUBE;  
Power Challenge and Power Indigo results are due to J. McDonald of SGI.


%%%%%%%%%%%%%%%%%%%
%%%%%% LU-A %%%%%%%%%
%%%%%%%%%%%%%%%%%%%
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|r|}
\hline
Computer System          &  Date    & No.   & Time   & Ratio to \\
                         & Received & Proc. & (sec.) & Y-MP/1 \\
\hline
\hline
BBN TC2000               & Dec 91   &  62   &  3032.0 &  0.11 \\
\hline
Convex SPP1000		 & Oct 94   &   1   &  2668.0 &  0.13 \\
                         &          &   4   &   597.0 &  0.56 \\
                         &          &   8   &   331.0 &  1.01 \\
                         &          &  16   &   209.0 &  1.60 \\
\hline
Cray Y-MP                & Aug 92   &   1   &  333.5  &  1.00 \\
                         &          &   8   &  49.5   &  6.74 \\
\hline
Cray EL                  & Aug 92   &   1   &  1449.0 &  0.23 \\
                         &          &   4   &  522.3  &  0.64 \\
                         &          &   8   &  351.6  &  0.95 \\
\hline
Cray C-90                & Aug 92   &   1   &  157.6  &  2.12 \\
                         &          &   4   &  43.9   &  7.59 \\
                         &          &  16   &  17.6   & 18.93 \\
\hline
Cray T3D                 & Oct 94   & 16    & 214.23   & 1.56 \\
                         &          & 32    & 111.82   & 2.98 \\ 
                         &          & 64    &  58.69   & 5.69 \\ 
                         &          & 128   &  30.38   & 10.98 \\ 
                         &          & 256   &  16.99   & 19.63 \\
                         &          & 512   &   9.59   & 34.78 \\
                         &          & 1024  &   7.09   & 47.04 \\
\hline
Fujitsu VPP500           & Aug 94   & 1     &  146.89 & 2.27 \\
\hline
IBM RS6000-590           & Mar 94   & 1     &  645.2  &  0.5 \\
\hline
IBM SP-1                 & Feb 94   &  8    &  291.4  &  1.1 \\
                         &          & 16    &  172.9  &  1.9 \\
                         &          & 32    &  101.8  &  3.3 \\
                         &          & 64    &  63.2   &  5.3 \\
\hline
IBM SP-2                 & Aug 94   &  8    &  116.23  &  2.87 \\
                         &          &  16   &   69.09  & 4.83 \\
                         &          &  32   &   38.90  & 8.57 \\
                         &          &  64   &   24.94  & 13.37 \\
\hline
Intel iPSC/860           & Mar 91   &  64   &  690.8  &  0.48 \\
                         &          & 128   &  442.5  &  0.75 \\
\hline
Intel Paragon (OSF1.2)   & Jul 94   & 64    &  190.0  & 1.76 \\
                         &          & 128   &  118.0  & 2.83 \\
                         &          & 256   &   75.0  & 4.45 \\
\hline
Kendall Square KSR1      & Feb 94   & 32    &  341.0  &  1.0 \\
                         &          & 64    &  199.0  &  1.7 \\
                         &          & 128   &  155.0  &  2.2 \\
\hline
Kendall Square KSR2      & Feb 94   & 32    &  172.0  &  1.9 \\
                         & May 94   & 64    &  102.0  &  3.27\\
\hline
\end{tabular}
\stepcounter{table}
\subcaption{Results for the Class A LU Simulated CFD Application (cont'd)}
\end{center} \end{table}

\addtocounter{subtable}{-1}
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|}
\hline
Computer System            &  Date    & No.   & Time   & Ratio to \\
                           &  Received& Proc. & (sec.) & Y-MP/1 \\
\hline
\hline
Kyoto/Matsushita ADENART & Feb 94  & 256    &  327.5  &  1.0 \\
\hline
MasPar MP-1              & Aug 92   &  4K   &  1580.0 & 0.2 \\
\hline
MasPar MP-2              & Nov 92   &  4K   &  463.5  & 0.7 \\
\hline
Meiko CS-1               & Aug 92   &  16   &  2937.0 &  0.1 \\
\hline
nCUBE-2S		 & Mar 94   &  64   &  1322.0 &   0.3 \\
                         &          & 128   &   712.5 &   0.5 \\
                         &          & 256   &   389.1 &   0.9 \\
                         &          & 512   &   226.1 &   1.5 \\
                         &          &1024   &   134.1 &   2.5 \\
\hline
Silicon Graphics         & Jul 94   &  1    &  604.0  &  0.55 \\
Power Challenge XL       &          &  4    &  231.8  &  1.44 \\
                         &          &  8    &  111.7  &  2.99 \\
                         &          &  16   &   65.3  &  5.11 \\
\hline
Silicon Graphics Power Indigo   & Oct 94   &  1    &  716.5  &  0.47 \\
\hline
Thinking Machines CM-2   & Mar 91   &  8K   &  1307.0 &  0.26 \\
                         &          & 16K   &  850.0  &  0.39 \\
                         &          & 32K   &  546.0  &  0.61 \\
\hline
Thinking Machines CM-5   & Aug 93   &  32   &  418.0  &  0.80 \\
                         &          &  64   &  272.0  &  1.23 \\
                         &          &  128  &  171.0  &  1.95 \\
\hline
Thinking Machines CM-5E  & Feb 94   & 32    &  152.0  &  2.2 \\
                         &          & 64    &  97.0   &  3.4 \\
                         &          & 128   &  65.0   &  5.1 \\
\hline
\end{tabular}
\subcaption{(cont'd) Results for the Class A LU Simulated CFD Application}
\end{center} \end{table}
%%%%%%%%%%%%%%%%%%%
%%%%%% LU-B %%%%%%%%%
%%%%%%%%%%%%%%%%%%%
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|r|}
\hline
Computer System          &  Date    & No.   & Time   & Ratio to \\
                         & Received & Proc. & (sec.) & C90/1 \\
\hline
\hline
Cray C90                 & Dec 93   & 1     & 648.5  &  1.00 \\
                         &          & 4     & 166.1  &  3.9 \\
                         &          & 16    & 51.6   & 12.6 \\
\hline
Cray T3D                 & Oct 94   & 16    & 875.49 &  0.74 \\
                         &          & 32    & 470.82 &  1.38 \\
                         &          & 64    & 241.14 &  2.69 \\
                         &          & 128   & 124.48 &  5.21 \\
                         &          & 256   &  66.03 &  9.82 \\
                         &          & 512   &  36.39 &  17.82 \\
                         &          & 1024  &  20.77 &  31.22 \\ 
\hline
Fujitsu VPP500           & Aug 94   & 1     & 591.05 &  1.10 \\
\hline
IBM RS6000-590           & Mar 94   & 1     & 2694.6 &  0.2 \\
\hline
IBM SP-1                 & Feb 94   & 16    & 604.8  &  1.1 \\
                         &          & 32    & 348.1  &  1.9 \\
                         &          & 64    & 207.5  &  3.1 \\
\hline
IBM SP-2                 & Aug 94   & 8     & 434.59 &  1.49 \\
                         &          & 16    & 238.72 &  2.72 \\
                         &          & 32    & 135.92 &  4.77 \\
                         &          & 64    &  79.64 &  8.14 \\
                         &          & 128   &  49.82 &  13.02 \\
\hline
Kendall Square KSR2      & May 94   & 64    & 424.0 & 1.53 \\
\hline
Intel Paragon (OSF1.2)   & Jul 94   & 64    & 675.0 & 0.96 \\
                         &          & 128   & 406.0 & 1.60 \\
                         &          & 256   & 254.0 & 2.55 \\
                         &          & 512   & 175.0 & 3.71 \\
\hline
Thinking Machines CM-5E  & Feb 94   & 32    & 595.0  & 1.1 \\
                         &          & 64    & 367.0  & 1.8 \\
                         &          & 128   & 318.0  & 2.0 \\
\hline
Silicon Graphics         & Jul 94   & 1     & 2617.9 & 0.25 \\
Power Challenge XL       &          & 4     & 1010.5 & 0.64 \\
                         &          & 8     &  550.2 & 1.18 \\
                         &          & 16    &  308.1 & 2.10 \\
\hline
\end{tabular}
\subcaption{Results for the Class B LU Simulated CFD Application}
\end{center} \end{table}

%%%%%%%%%%%%%%%%%%%
%%%%%% SP-A %%%%%%%%%
%%%%%%%%%%%%%%%%%%%
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|r|}
\hline
Computer System          &  Date    & No.   & Time   & Ratio to \\
                         & Received & Proc. & (sec.) & Y-MP/1 \\
\hline
\hline
BBN TC2000               & Dec 91   &  112  &  880.0 &  0.54 \\
\hline
Convex SPP1000           & Oct 94   &   1   & 2813.0 &  0.17 \\
                         &          &   4   &  751.0 &  0.63 \\
                         &          &   8   &  379.0 &  1.24 \\
                         &          &  16   &  250.0 &  1.89\\
\hline
Cray Y-MP                & Aug 92   &    1  &  471.5 &  1.00 \\
                         &          &    8  &  64.6  &  7.30 \\
\hline
Cray EL                  & Aug 92   &    1  &  2025.7 &  0.23 \\
                         &          &    4  &  601.9 &  0.78 \\
                         &          &    8  &  488.4 &  0.97 \\
\hline
Cray C-90                & Aug 92   &    1  &  184.70 &  2.55 \\
                         &          &    4  &  49.74 &  9.48 \\
                         &          &   16  &  13.06 & 36.10 \\
\hline
Cray T3D                 & Jul 94   & 16    &  206.08 & 2.29 \\
                         &          & 32    &  107.54 & 4.38 \\
                         &          & 64    &  55.39  & 8.51 \\
                         &          & 128   &  28.58  & 16.50 \\
                         &          & 256   &  15.31  & 30.80 \\
                         & Aug 94   & 512   &  8.91   & 52.92 \\
                         & Oct 94   & 1024  &  5.41   & 87.15 \\
\hline
Fujitsu VPP500           & Aug 94   & 1     &  176.75 & 2.67 \\
                         &          & 2     &  108.85 & 4.33 \\ 
                         &          & 4     &  57.24  & 8.24 \\ 
                         &          & 8     &  29.87  & 15.79 \\ 
                         &          & 16    &  20.99  & 22.47 \\ 
\hline
IBM RS6000-590          & Mar 94   & 1     &  993.1 & 0.5 \\
\hline
IBM SP-1                 & Feb 94   &  8    &  441.6 &   1.1 \\
                         &          & 16    &  268.7 &   1.8 \\
                         &          & 32    &  165.0 &   2.9 \\
                         &          & 64    &  100.4 &   4.7 \\
\hline
IBM SP-2                 & Aug 94   &  8    &  177.39 & 2.65 \\
                         &          &  16   &  100.19 & 4.71 \\
                         &          &  32   &   58.00 & 8.13 \\
                         &          &  64   &   34.77 & 13.56 \\
\hline
Intel iPSC/860           & Jul 94   &   64  &  640.0 &  0.74 \\
                         & Aug 92   &  128  &  449.5 &  1.05 \\
\hline
Intel Paragon (OSF1.2)   & Jul 94   &   64  &  226.0    & 2.09\\
                         &          &   128 &  143.0    & 3.30\\
                         &          &   256 &  97.0$^{**}$ & 4.86$^{**}$\\
                         &          &   324 &  89.0$^{**}$ & 5.30$^{**}$\\
\hline
Kendall Square KSR1      & Feb 94   & 32    &  418.0 &   1.1 \\
                         &          & 64    &  257.0 &   1.8 \\
                         &          & 128   &  160.0 &   2.9 \\
\hline
Kendall Square KSR2      & Feb 94   & 32    &  221.0 &   2.1 \\
                         & May 94   & 64    &  131.0 &   3.6 \\
\hline
\end{tabular} 
\stepcounter{table}
\subcaption{Results for the Class A SP Simulated CFD Application (cont'd)
($^*$ indicates library result; $^{**}$~indicates multipartition algorithm
instead of transpose algorithm).}
\end{center} \end{table}

\addtocounter{subtable}{-1}
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|}
\hline
Computer System            &  Date    & No.   & Time   & Ratio to \\
                           &  Received& Proc. & (sec.) & Y-MP/1 \\
\hline
\hline
Kyoto/Matsushita ADENART & Feb 94   & 256   &  209.9 &   2.3 \\
\hline
MasPar MP-1              & Aug 92   &   4K  &  1772 &  0.27 \\
\hline
MasPar MP-2              & Nov 92   &   4K  &  615 &  0.77 \\
\hline
Meiko CS-1               & Aug 92   &   16  &  2975 &  0.16 \\
\hline
nCUBE-2S		 & Mar 94   &   64  & 1243.2 & 0.4 \\
                         &          &  128  &  717.4 & 0.7 \\
                         & Jul 94   &  256  &  387.3 & 1.22 \\
                         &          &  512  &  208.6 & 2.26 \\
                         &          & 1024  &  120.9 & 3.90 \\
\hline
NEC SX-3                 & Oct 94   &  1    & 75.72  & 6.23 \\
\hline
Silicon Graphics         & Jul 94   & 1     &  858.3     &  0.55 \\
Power Challenge XL       &          & 4     &  225.8     &  2.09 \\
                         &          & 8     &  119.5     &  3.94 \\
                         &          & 16    &  67.2      &  7.01 \\
\hline
Silicon Graphics Power Indigo   & Oct 94   & 1     &  986.8     & 0.48 \\
\hline
Thinking Machines CM-2   & Dec 91   &  16K  & $1444.0^*$ & 0.33 \\
                         &          &  32K  & $917.0^*$  & 0.51 \\
                         &          &  64K  & $640.0^*$  & 0.74\\
\hline
Thinking Machines CM-5   & May 93   &   32  &  289.0     &  1.63 \\
                         &          &   64  &  170.0     &  2.77  \\
                         &          &   128 &  119.0     &  3.96  \\
\hline
Thinking Machines CM-5E  & Feb 94   & 32    &  169.0     &   2.8 \\
                         &          & 64    &  104.0     &   4.5 \\
                         &          & 128   &   61.0     &   7.7 \\
\hline
\end{tabular} 
\subcaption{(cont'd) Results for the Class A SP Simulated CFD Application 
($^*$ indicates library result; $^{**}$~indicates multipartition algorithm
instead of transpose algorithm).}
\end{center} \end{table}

%%%%%%%%%%%%%%%%%%%
%%%%%% SP-B %%%%%%%%%
%%%%%%%%%%%%%%%%%%%
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|r|}
\hline
Computer System          &  Date    & No.   & Time   & Ratio to \\
                         & Received & Proc. & (sec.) & C90/1 \\
\hline
\hline
Convex SPP1000           & Oct 94   &   8   & 1739.0 &  0.41 \\
\hline
Cray C90                 & Dec 93   & 1     & 713.1  & 1.00 \\
                         &          & 4     & 203.1  & 3.5 \\
                         &          & 16    & 80.4   & 8.9 \\
\hline
Cray T3D                 & Jul 94   & 16    & 818.07  & 0.87 \\
                         &          & 32    & 463.62  & 1.54 \\
                         &          & 64    & 242.69  & 2.94 \\
                         &          & 128   & 130.45  & 5.47 \\
                         &          & 256   & 77.29   & 9.23 \\
                         & Oct 94   & 512   & 42.63   & 16.73 \\
                         &          & 1024  & 25.23   & 28.26 \\
\hline
Fujitsu VPP500           & Aug 94   & 1     & 664.76  & 1.07 \\
                         &          & 2     & 417.78  & 1.71 \\
                         &          & 4     & 228.37  & 3.12 \\
                         &          & 6     & 143.20  & 4.98 \\
                         &          & 8     & 120.05  & 5.94 \\
                         &          & 17    & 53.12   & 13.42 \\
                         & Sep 94   & 34    & 39.01   & 18.28 \\
\hline
IBM RS6000-590           & Mar 94   & 1     & 4047.2 & 0.2 \\
\hline
IBM SP-1                 & Feb 94   & 16    & 941.2  & 0.8 \\
                         &          & 32    & 522.4  & 1.4 \\
                         &          & 64    & 302.3  & 2.5 \\
\hline
IBM SP-2                 & Aug 94   & 8    & 701.66  & 1.02 \\
                         &          & 16   & 368.02  & 1.94 \\
                         &          & 32   & 194.19  & 3.67 \\
                         &          & 64   & 111.19  & 6.41 \\
                         & Oct 94   & 128  & 63.86   & 11.17\\
\hline
Intel Paragon (OSF1.2)   & Mar 94   & 64    & 960.0 & 0.7  \\
                         & Jul 94   & 102   & 610.0 & 1.17 \\
                         &          & 204   & 387.0 & 1.84 \\
                         &          & 256   & 301.0$^*$ & 2.37$^*$ \\
                         &          & 324   & 262.0$^*$ & 2.72$^*$ \\
                         &          & 400   & 246.0$^*$ & 2.90$^*$ \\
                         &          & 484   & 209.0$^*$ & 3.41$^*$ \\
\hline
Kendall Square KSR2      & May 94   & 64    &  495.0 &   1.44 \\
\hline
NEC SX-3                 & Oct 94   & 1     & 294.68 & 2.42 \\
\hline
Silicon Graphics         & Jul 94   & 1     & 3719.5 & 0.19 \\ 
Power Challenge XL       &          & 4     &  947.6 & 0.75 \\
                         &          & 8     &  491.4 & 1.45 \\
                         &          & 16    &  313.1 & 2.28 \\
\hline
Thinking Machines CM-5E  & Feb 94   & 32    & 1014.0 & 0.7 \\
                         &          & 64    & 595.0  & 1.2 \\
                         &          & 128   & 320.0  & 2.2 \\
\hline
\end{tabular} 
\subcaption{Results for the Class B SP Simulated CFD Application
($^*$ indicates multipartition algorithm instead of transpose algorithm).}
\end{center} \end{table}

%%%%%%%%%%%%%%%%%%%
%%%%%% BT %%%%%%%%%
%%%%%%%%%%%%%%%%%%%
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|r|}
\hline
Computer System         &  Date    & No.   & Time   & Ratio to \\
                        & Received & Proc. & (sec.) & Y-MP/1 \\
\hline
\hline
BBN TC2000              & Dec 91   & 112   &  1378.0 &  0.58 \\
\hline
Convex SPP1000          & Oct 94   &   1   &  2825.0 & 0.28 \\
                        &          &   4   &   732.0 & 1.08 \\
                        &          &   8   &   366.0 & 2.17 \\
                        &          &  16   &   211.0 & 3.76 \\
\hline
Cray Y-MP               & Aug 92   &   1   &  792.4 &  1.00 \\
                        &          &   8   &  114.0 &  6.95 \\
\hline
Cray EL                 & May 93   &   1   &  3832.8  &  0.21 \\
                        &          &   4   &  1090.2  &  0.73 \\
                        &          &   8   &  764.1   &  1.04 \\
\hline
Cray C-90               & Aug 92   &   1   &  356.9 &  2.22 \\
                        &          &   4   &  96.1 &  8.25 \\
                        &          &  16   &  28.4 & 27.91 \\
\hline
Cray T3D                & Oct 94   & 16    &  234.12 & 3.38 \\
                        &          & 32    &  117.69 & 6.72 \\
                        &          & 64    &  60.55  & 13.09 \\
                        & Jul 94   & 128   &  30.84  & 25.69 \\
                        &          & 256   &  15.89  & 49.87 \\
                        & Aug 94   & 512   &   8.39  & 94.45 \\
                        & Oct 94   & 1024  &   4.56  & 173.77 \\
\hline
Fujitsu VPP500          & Oct 94   & 2     &  75.17 & 10.54 \\
                        &          & 4     &  39.14 & 20.25 \\ 
                        &          & 8     &  19.82 & 39.98 \\ 
                        &          & 16    &  9.99  & 79.32 \\
                        &          & 32    &  5.09  & 155.68 \\
                        &          & 64    &  2.66  & 297.89 \\ 
\hline
IBM RS6000-590          & Feb 94   & 1     &  1249.4 &   0.6 \\
\hline
IBM SP-1                & Aug 94   &  8    &   443.9 & 1.78 \\
                        &          & 16    &   249.2 & 3.18 \\
                        &          & 32    &   143.0 & 5.54 \\
                        &          & 64    &   83.1 &  9.53 \\
\hline
IBM SP-2                & Aug 94   &  8    & 226.23  & 3.35 \\
                        &          &  16   & 128.11  & 6.18 \\
                        &          &  32   & 69.72   & 11.36 \\
                        &          &  64   & 39.87   & 19.87 \\
\hline
\end{tabular}
\stepcounter{table}
\subcaption{Results for the Class A BT Simulated CFD Application ($^*$ indicates library
result) (cont'd).}
\end{center} \end{table}

\addtocounter{subtable}{-1}
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|r|}
\hline
Computer System         &  Date    & No.   & Time   & Ratio to \\
                        & Received & Proc. & (sec.) & Y-MP/1 \\
\hline
\hline
Intel iPSC/860          & Aug 92   &  64   &  714.7 &  1.11 \\
                        &          & 128   &  414.3 &  1.91 \\
\hline
Intel Paragon (OSF1.2)   & Mar 94   &   64  &  235.0 & 3.4\\
                         &          &  128  &  129.0 & 6.1\\
                         &          &  256  &  83.0  & 9.5\\
                         &          &  512  &  63.0  & 12.5\\
\hline
Intel Paragon (SunMos)  & Nov 93   & 64    &  224.0  &  3.5\\
                        & Mar 94   & 128   &  113.0  &  7.0\\
\hline
Kendall Square KSR1     & Feb 94   & 32    &  457    &  1.7\\
                        &          & 64    &  256    &  3.1\\
                        &          & 128   &  145    &  5.5\\
\hline
Kendall Square KSR2     & Feb 94   & 32    &  225    &  3.5\\
                        & May 94   & 64    &  130    &  6.10 \\
\hline
Kyoto/Matsushita ADENART& Feb 94   &256    &  314.1  &  2.5\\
\hline
MasPar MP-1             & Aug 92   & 4K    &  2396.0 &  0.33 \\
\hline
MasPar MP-2             & Nov 92   & 4K    &  789.0 &  1.00 \\
\hline
Meiko CS-1              & Aug 92   & 16    &  2984.0 &  0.27 \\
\hline
Meiko CS-2              & Oct 94   & 8     &  570.4  & 1.39 \\
                        &          & 16    &  286.6  & 2.77 \\
                        &          & 32    &  149.3  & 5.31 \\
\hline
nCUBE-2S		& Mar 94   &    64  & 1243.2  &  0.6  \\
                        &          &   128  &  644.7  &  1.2 \\
                        & Jul 94   &   256  &  336.7  &  2.35 \\
                        &          &   512  &  179.1  &  4.42 \\
                        &          &  1024  &  100.9  &  7.85 \\
\hline
NEC SX-3                & Oct 94   &  1    &  100.31  & 7.90 \\
\hline
Silicon Graphics        & Jul 94   & 1     &  1330.3  & 0.60 \\
Power Challenge XL      &          & 4     &   355.9  & 2.23 \\
                        &          & 8     &   177.0  & 4.48 \\
                        &          & 16    &   91.8   & 8.63 \\
\hline
Silicon Graphics Power Indigo& Oct 94   & 1     &  1499.6  & 0.53 \\
\hline
Thinking Machines CM-2  & Dec 91   & 16K   &  $1118.0^*$ &  0.71 \\
                        &          & 32K   &  $634.0^*$  &  1.25 \\
                        &          & 64K   &  $370.0^*$  &  2.14 \\
\hline
Thinking Machines CM-200& Dec 91   & 16K   &  $832.0^*$  & 0.95 \\
                        &          & 32K   &  $601.0^*$  & 1.32 \\
\hline
Thinking Machines CM-5  & May 93   & 32    &  284.0  &  2.79 \\
                        &          & 64    &  175.0  &  4.50 \\
                        &          & 128   &  119.0  &  6.66 \\
\hline
Thinking Machines CM-5E & Feb 94   & 32    &   146.0 &   5.4\\
                        &          & 64    &    84.0 &   9.4\\
                        &          & 128   &    48.0 &  16.5\\
\hline
\end{tabular}
%%%\stepcounter{table}
\subcaption{(cont'd) Results for the Class A BT Simulated CFD Application ($^*$ indicates library
result).}
\end{center} \end{table}
%%%%%%%%%%%%%%%%%%%
%%%%%% BT-B %%%%%%%%%
%%%%%%%%%%%%%%%%%%%
\begin{table} \begin{center}
\begin{tabular}{|l|r|r|r|r|r|r|}
\hline
Computer System         &  Date    & No.   & Time   & Ratio to \\
                        & Received & Proc. & (sec.) & C90/1 \\
\hline
\hline
Convex SPP1000          & Oct 94   &   8   &  1606.0 & 0.79 \\
\hline
Cray C90                & Dec 93   & 1     & 1261.4 & 1.00\\
                        &          & 4     & 324.9  & 3.9\\
                        &          & 16    & 96.4   & 13.1\\
\hline
Cray T3D                & Oct 94   & 16    & 918.04 & 1.37 \\
                        &          & 32    & 487.33 & 2.59 \\
                        &          & 64    & 254.82 & 4.95 \\
                        &          & 128   & 132.27 & 9.54 \\
                        &          & 256   & 69.39  & 18.18 \\
                        & Jul 94   & 512   & 38.01  & 33.19 \\
                        & Oct 94   & 1024  & 20.45  & 61.68 \\
\hline
Fujitsu VPP500          & Oct 94   & 17    & 37.26 & 33.85 \\
                        &          & 34    & 18.82 & 67.02 \\
                        &          & 51    & 12.61 & 100.03 \\
\hline
IBM RS6000-590          & Mar 94   & 1     & 5242.4 & 0.2\\
\hline
IBM SP-1                & Apr 94   & 16    & 987.4  & 1.28 \\
                        &          & 32    & 511.2  & 2.47 \\
                        &          & 64    & 274.6  & 4.59 \\
\hline
IBM SP-2                & May 94   & 8    & 976.91 & 1.29 \\
                        &          & 16   & 498.49 & 2.53 \\
                        &          & 32   & 257.52 & 4.90 \\
                        &          & 64   & 135.98 & 9.28 \\
                        & Oct 94   & 128  & 75.41  & 16.73 \\
\hline
Intel Paragon (OSF1.2)  & Mar 94   & 102   & 633.0  &  2.0\\
                        &          & 204   & 359.0  &  3.5\\
                        &          & 306   & 257.0  &  4.9\\
                        &          & 408   & 226.0  &  5.6\\
                        &          & 510   & 196.0  &  6.4\\
\hline
Intel Paragon (SunMos)  & Mar 94   & 102   & 598.0  & 2.1\\
                        &          & 204   & 324.0  & 3.9\\
                        &          & 306   & 215.0  & 5.9\\
\hline
Kendall Square KSR2     & May 94   & 64    & 542.0  & 2.33 \\
\hline
NEC SX-3                & Oct 94   & 1     & 399.11 & 3.16 \\
\hline
Silicon Graphics        & Jul 94   & 1     & 5698.7 & 0.22 \\
Power Challenge XL      &          & 4     & 1450.0 & 0.87 \\
                        &          & 8     & 775.0  & 1.63 \\
                        &          & 16    & 426.0  & 2.96 \\
\hline
Thinking Machines CM-5E & Feb 94   & 32    & 806.0  &  1.6\\
                        &          & 64    & 464.0  &  2.7\\
                        &          & 128   & 253.0  &  5.0\\
\hline
\end{tabular}
\subcaption{Results for the Class B BT Simulated CFD Application}
\end{center} \end{table}


\section{Sustained Performance Per Dollar}

One aspect of the relative performance of these systems has not been
addressed so far, namely the differences in price between these
systems.  One way to compensate for these price differences is to compute
sustained performance per million dollars, i.e. the performance ratio
figures shown in Tables 2 through 9 divided by the list price in
millions.  Some figures of this type are shown in Table 11 for two of
the benchmarks (the Class B size MG and SP benchmarks) for the most
recent of the systems tested.  The table includes the list price of
the minimal system (in terms of memory per node, disk space, etc.)
required to run the full Class B size NPB as implemented by the vendor.
These prices were provided by the vendors and include any associated
software costs (i.e. operating system, compilers, scientific libraries
as required, etc.) but do not include maintenance.
Hardware configurations for the various systems as tested by the vendors 
and associated list prices are provided in Table 10.
Be aware that list prices are similar to peak performance in that they
are guaranteed not to be exceeded.  

\begin{table}[htb] \begin{center} 
\begin{tabular}{lllrrr}
Computer System 	& No. PE& Memory         & Disk  & List Price & Date \\
\hline
\hline
Convex SPP1000          & 16    & 64 MB/PE       &       & 0.94M     & Jul 94\\
Cray C90		& 16    & 256 MW (total) &       &30.90M     & Oct 93\\
Cray EL98               & 8     & 1 GB (total)   & 12 GB & 1.11M     & Oct 93\\
Cray T3D                & 256   & 16 MB/PE       &       & 9.25M     & Mar 94\\
Fujitsu VPP500          & 16    & 256 MB/PE      &       & 17.0M     & Mar 94\\
IBM SP-1                & 64    & 64 MB/PE       & 64 GB & 2.66M     & Oct 93\\
IBM SP-2                & 64    & 128 MB/PE (wide)& 64 GB & 5.94M     & Oct 94\\
IBM RS6000-590          & 1     & 1 GB           &       & 0.25M     & Mar 94\\
Intel Paragon           & 256   & 32 MB/PE       &       & 7.49M     & Mar 94\\
Kendall Square KSR1     & 128   & 32 MB/PE       & 25 GB & 1.7M     & Mar 94\\
Kendall Square KSR2     & 32    & 32 MB/PE       & 25 GB & 1.43M     & Mar 94\\
MasPar MP-2             & 16K   & 1 GB (total)   &       & 1.61M     & Oct 93\\
nCUBE-2S                & 1024  & 4 MB/PE        &       & 4.0M     & Mar 94\\
NEC SX-3/14R            & 1     & 2 GB           &       & 4.1M     & Oct 94\\
SGI Power Challenge     & 16    & 2 GB (total)   & 2 GB  & 1.02M     & Jun 94\\
Thinking Machines CM-5E & 128   & 32 MB/PE       &       & 4.0M     & Mar 94\\
\hline
\end{tabular} 
\caption{U.S. List Price for systems configured as tested.}
\end{center} \end{table}

\begin{table}[htb] \begin{center} 
\begin{tabular}{|l|l|r|r|r|r|r|}
\hline
        &                       & No.   & Ratio to & Nominal & Date   & Perf. per  \\
B'mark  & Computer System       & Proc. & C90/1   & cost (\$)&        & million \$ \\
\hline
\hline
MG-B    & Cray C-90             &   16  &    9.5   &  30.90M & Dec 93 & 0.31\\
        & Cray T3D              &  256  &    10.5  &  9.25M  & Oct 94 & 1.13\\
        & Fujitsu VPP500        &   16  &    16.1  &  17.00M & Oct 94 & 0.95\\
        & IBM RS6000-590        &    1  &    0.2   &  0.25M  & Mar 94 & 0.82\\
        & IBM SP-1              &   64  &    2.7   &  2.66M  & Mar 94 & 1.03\\
        & IBM SP-2              &   64  &    8.3   &  5.43M  & Aug 94 & 1.54\\
        & Intel Paragon (OSF1.2)&  256  &    2.8   &  7.49M  & Mar 94 & 0.37\\
     	& NEC SX-3              &   1   &    2.9   &  4.10M  & Oct 94 & 0.70\\
        & Thinking Machines CM-5E& 128  &    5.6   &  4.00M  & Feb 94 & 1.40\\
\hline
SP-B    & Convex SPP1000        &   16  &   0.4    &  0.94M  & Oct 94 & 0.44\\
        & Cray C-90             &   16  &   8.9    &  30.90M & Dec 93 & 0.29\\
        & Cray T3D              &  256  &   9.2    &  9.25M  & Jul 94 & 1.00\\
        & Fujitsu VPP500        &   17  &   13.42  &  18.06M & Aug 94 & 0.74\\
        & IBM RS6000-590        &    1  &   0.18   &  0.25M  & Mar 94 & 0.70\\
        & IBM SP-1              &   64  &   2.5    &  2.66M  & Feb 94 & 0.94\\
        & IBM SP-2              &   64  &   6.4    &  5.43M  & Aug 94 & 1.18\\
        & Intel Paragon         &  256  &   2.4    &  7.49M  & Jul 94 & 0.32\\
	& NEC SX-3              &   1   &   2.4    &  4.10M  & Oct 94 & 0.59\\
	& SGI Power Challenge   &  16   &   2.3    &  1.02M  & Jul 94 & 2.25\\
        & Thinking Machines CM-5E& 128  &   2.2    &  4.00M  & Feb 94 & 0.55\\
\hline
\end{tabular} 
\caption{Approximate Sustained Performance Per Dollar on Two Class B Benchmarks}
\end{center} \end{table}


\vfill
\newpage
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\end{document}



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