LINPACK_BENCH
The LINPACK Benchmark

LINPACK_BENCH is a FORTRAN90 program which carries out the LINPACK Benchmark.

The LINPACK benchmark is a test problem used to rate the performance of a computer on a simple linear algebra problem.

The test problem requires the user to set up a random dense matrix A of size N = 1000, and a right hand side vector B which is the product of A and a vector X of all 1's. The first task is to compute an LU factorization of A. The second task is to use the LU factorization to solve the linear system

A * X = B.

The number of floating point operations required for these two tasks is roughly

ops = 2 * N*N*N / 3 + 2 * N * N,

mflops = ops / ( cpu * 1000000 ).

On a given computer, if you run the benchmark for a sequence of increasing values of N, the behavior of the MegaFLOPS rating will vary as you pass through three main zones of behavior:

• a rising zone, as both the local cache memory and the processor are not challenged.
• a flat zone, where the processor is challenged, that is, it is performing at top efficiency.
• a decaying zone, where the local cache memory is also challenged, that is the matrix is so large that the cache is not big enough to keep the necessary data close enough to the processor to keep it running at top speed.

Language	Precision	Type	Machine	Comment	MegaFLOPS
Fortran90	Single	Real	Chili	(rewritten)	240
Fortran90	Single	Real	Kachina		196
Fortran90	Single	Real	Chili		194
Fortran90	Single	Real	Eclipse	(1 processor)	127
Fortran90	Single	Real	DHCP95 (Apple G5)	gfortran	118
Fortran90	Single	Real	Yankee (Apple G4)		36
Fortran90	Single	Real	Teragold	(1 processor)	18
Fortran90	Single	Real	Sgi		16
Fortran90	Double	Real	DHCP95 (Apple G5)	gfortran	149
Fortran90	Double	Real	Chili	fort -fast	104
Fortran90	Double	Real	Kachina		87
Fortran90	Double	Real	Chili		77
Fortran90	Quad	Real	DHCP95 (Apple G5)	gfortran	23
Fortran90	Quad	Real	Chili		10

Languages:

LINPACK_BENCH is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

LINPACK_D, a FORTRAN90 library which supplies the solvers used by LINPACK_BENCH.

LINPACK_Q, a FORTRAN90 library which implements a few of the LINPACK library of linear solvers, using quadruple precision.

MATMUL, a FORTRAN90 program which is an interactive matrix multiplication benchmark program.

MDBNCH, a FORTRAN77 program which is a benchmark code for a molecular dynamics calculation.

MEMORY_TEST, a FORTRAN90 program which declares and uses a sequence of larger and larger vectors, to see how big a vector can be used on a given machine and compiler.

MXM, a FORTRAN90 program which sets up a matrix multiplication problem A=B*C of arbitrary size, and compares the time required for IJK, IKJ, JIK, JKI, KIJ and KJI orderings of the loops.

MXV, a FORTRAN90 program which compares the performance of (DO I, DO J) loops, (DO J, DO I) loops, and MATMUL for computing the product of an MxN matrix A and an N vector X.

NAS, a FORTRAN90 program which runs the NASA kernel benchmark.

SUM_MILLION, a FORTRAN90 program which sums the integers from 1 to 1,000,000, as a demonstration of how to rate a computer's speed;

TIMER, a FORTRAN90 example which demonstrates how to measure CPU time or elapsed time.

Reference:

1. http://www.netlib.org/benchmark/1000s the LINPACK benchmark website (single precision).
2. http://www.netlib.org/benchmark/1000d the LINPACK benchmark website (double precision).
3. Jack Dongarra,
   Performance of Various Computers Using Standard Linear Equations Software, Technical Report CS-89-85,
   Electrical Engineering and Computer Science Department,
   University of Tennessee, 2008.
4. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
   LINPACK User's Guide,
   SIAM, 1979,
   ISBN13: 978-0-898711-72-1,
   LC: QA214.L56.
5. George Fishman,
   Multiplicative congruential random number generators with modulus 2**b: an exhaustive analysis for b = 32 and a partial analysis for b = 48,
   Mathematics of Computation,
   Volume 189, 1990, pages 331-344.
6. Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
   Algorithm 539: Basic Linear Algebra Subprograms for Fortran Usage,
   ACM Transactions on Mathematical Software,
   Volume 5, Number 3, September 1979, pages 308-323.

Source Code:

LINPACK_BENCH_S is the single precision version:

• linpack_bench_s.f90, the source code.
• linpack_bench_s.ll, commands to compile and load the source code on a system that uses IBM's LoadLeveler batch queueing system.
• linpack_bench_s_chili.txt, the output from an ALPHA named "Chili".
• linpack_bench_s_dhcp95.txt, the output from an Apple G5 named "DHCP95".
• linpack_bench_s_eclipse.txt, the output from one (Power4) processor of ECLIPSE, an IBM pSeries 690.
• linpack_bench_s_kachina.txt, the output from an ALPHA named "Kachina".
• linpack_bench_s_sgi.txt, the output from an SGI.
• linpack_bench_s_teragold.txt, the output from one (Power3) processor of TERAGOLD, an IBM pSeries 690.

LINPACK_BENCH_D is the double precision version:

• linpack_bench_d.f90, the source code.
• linpack_bench_d_chili.txt, the output an ALPHA named "Chili".
• linpack_bench_d_dhcp95.txt, the output from an Apple G5 named "DHCP95".
• linpack_bench_d_kachina.txt, the output from an ALPHA named "Kachina".

LINPACK_BENCH_Q is the quad precision version (your compiler might not allow this arithmetic type, or you may have to change the syntax of the program to get it):

• linpack_bench_q.f90, the source code.
• linpack_bench_q_chili.txt, the output from an ALPHA named "Chili".
• linpack_bench_q_dhcp95.txt, the output from an Apple G5 named "DHCP95".

List of Routines:

This is the list of routines for the double precision version of the benchmark program. The single and quad precision names are similar.

• LINPACK_BENCH_D drives the double precision LINPACK benchmark program.
• D_MATGEN generates a random matrix.
• D_RANDOM returns a uniformly distributed random number between 0 and 1.
• DAXPY adds a constant times one vector to another.
• DGEFA factors a real matrix.
• DGESL solves a real general linear system A * X = B.
• IDAMAX finds the index of the vector element of maximum absolute value.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.