LINPACK_BENCH
The LINPACK Benchmark

LINPACK_BENCH is a C program which carries out the LINPACK benchmark program.

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 ).

The C source code presented here is unusual in that a single file embodies both single and double precision. The precision to be used is specified at compile time with a compiler option. Moreover, another compiler option allows the user to request "rolled loops" (the normal kind of for loop), or "unrolled loops", in which the loops are done with an increment greater than 1. The unrolled option can often significantly improve performance.

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
C	Single	Real	DHCP95 (Apple G5)	rolled	108
C	Single	Real	DHCP95 (Apple G5)	unrolled	184
C	Double	Real	DHCP95 (Apple G5)	rolled	111
C	Double	Real	DHCP95 (Apple G5)	unrolled	190

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

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

Related Data and Programs:

LINPACK, a C++ library which supplies the solvers used by LINPACK_BENCH.

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 C++ 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 C 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.

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

TIMER, a C 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.c, the source code.

Examples and Tests:

• linpack_bench_dhcp95_output.txt, the output from an Apple Power5 named "dhcp95".

List of Routines:

• MAIN is the main program for LINPACK_BENCH.
• CPU_TIME reports the elapsed CPU time.
• DAXPY computes constant times a vector plus a vector.
• DDOT forms the dot product of two vectors.
• DGEFA factors a real general matrix.
• DGESL solves a real general linear system A * X = B.
• DSCAL scales a vector by a constant.
• IDAMAX finds the index of the vector element of maximum absolute value.
• R8_ABS returns the absolute value of a R8.
• R8_EPSILON returns the R8 round off unit.
• R8_MAX returns the maximum of two R8's.
• R8_RANDOM returns a uniformly distributed random number between 0 and 1.
• R8MAT_GEN generates a random R8MAT.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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