linpack_bench

linpack_bench, a Fortran90 code 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

Licensing:

The information on this web page is distributed under the MIT license.

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_bench_test

linpack_d, a Fortran90 code which supplies the solvers used by LINPACK_BENCH.

matmul, a Fortran90 code which is an interactive matrix multiplication benchmark program.

memory_test, a Fortran90 code 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 code 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.

nas, a Fortran90 code which runs the NASA kernel benchmark.

timer, a Fortran90 code which measures CPU time or elapsed time.

Reference:

1. https://www.netlib.org/benchmark/1000s the LINPACK benchmark website (single precision).
2. https://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.f90, the source code.
• linpack_bench.sh, compiles the source code.