The LINPACK Benchmark

LINPACK_BENCH is a C++ 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,
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:

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


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


LINPACK_BENCH is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a JAVA version and a MATLAB version.

Related Data and Programs:

LINPACK_D, a C++ library which solves linear systems using double precision real arithmetic;

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++ library which demonstrates how to measure CPU time or elapsed time.


  1. the LINPACK benchmark website (single precision).
  2. 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 of the program.

LINPACK_BENCH_D is the double precision version of the program.

List of Routines:

Here are the routines for the double precision version of the program:

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

Last revised on 07 March 2008.