linpack_bench


linpack_bench, a C++ 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,
therefore, the "MegaFLOPS" rating, or millions of floating point operations per second, can be found as
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:

LanguagePrecisionTypeMachineCommentMegaFLOPS
C++SingleRealDHCP95 (Apple G5)g++222
      
C++DoubleRealDHCP95 (Apple G5)g++167
C++DoubleRealchili (ALPHA)g++51

Licensing:

The computer code and data files described and made available on this web page are 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 C++ code which solves linear systems using double precision real arithmetic;

MEMORY_TEST, a C++ 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 C++ 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.

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

TIMER, a C++ code which demonstrates how to measure 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:


Last revised on 26 March 2020.