linpack_bench/linpack_bench.html

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    <title>
      LINPACK_BENCH - The LINPACK Benchmark
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      LINPACK_BENCH <br> The LINPACK Benchmark
    </h1>

    <hr>

    <p>
      <b>LINPACK_BENCH</b>
      is a FORTRAN90 program which
      carries out the LINPACK Benchmark.
    </p>

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

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

    <p>
      The number of floating point operations required for these two
      tasks is roughly
      <blockquote>
        ops = 2 * N*N*N / 3 + 2 * N * N,
      </blockquote>
      therefore, the "MegaFLOPS" rating, or millions of floating point
      operations per second, can be found as
      <blockquote>
        mflops = ops / ( cpu * 1000000 ).
      </blockquote>
    </p>

    <p>
      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:
      <ul>
        <li>
          a <i>rising</i> zone, as both the local cache memory and the processor
          are not challenged.
        </li>
        <li>
          a <i>flat</i> zone, where the processor is challenged, that is, it is
          performing at top efficiency.
        </li>
        <li>
          a <i>decaying</i> 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.
        </li>
      </ul>
    </p>

    <p>
      <table border="1">
        <tr>
          <th>Language</th><th>Precision</th><th>Type</th><th>Machine</th><th>Comment</t><th>MegaFLOPS</th>
        </tr>
        <tr>
          <td>Fortran90</td><td>Single</td><td>Real</td><td>Chili</td><td>(rewritten)</td><td>240</td>
        </tr>
        <tr>
          <td>Fortran90</td><td>Single</td><td>Real</td><td>Kachina</td><td>&nbsp;</td><td>196</td>
        </tr>
        <tr>
          <td>Fortran90</td><td>Single</td><td>Real</td><td>Chili</td><td>&nbsp;</td><td>194</td>
        </tr>
        <tr>
          <td>Fortran90</td><td>Single</td><td>Real</td><td>Eclipse</td><td>(1 processor)</td><td>127</td>
        </tr>
        <tr>
          <td>Fortran90</td><td>Single</td><td>Real</td><td>DHCP95 (Apple G5)</td><td>gfortran</td><td>118</td>
        </tr>
        <tr>
          <td>Fortran90</td><td>Single</td><td>Real</td><td>Yankee (Apple G4)</td><td>&nbsp;</td><td>36</td>
        </tr>
        <tr>
          <td>Fortran90</td><td>Single</td><td>Real</td><td>Teragold</td><td>(1 processor)</td><td>18</td>
        </tr>
        <tr>
          <td>Fortran90</td><td>Single</td><td>Real</td><td>Sgi</td><td>&nbsp;</td><td>16</td>
        </tr>

        <tr>
          <td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td>
        </tr>


        <tr>
          <td>Fortran90</td><td>Double</td><td>Real</td><td>DHCP95 (Apple G5)</td><td>gfortran</td><td>149</td>
        </tr>
        <tr>
          <td>Fortran90</td><td>Double</td><td>Real</td><td>Chili</td><td>fort -fast</td><td>104</td>
        </tr>
        <tr>
          <td>Fortran90</td><td>Double</td><td>Real</td><td>Kachina</td><td>&nbsp;</td><td>87</td>
        </tr>
        <tr>
          <td>Fortran90</td><td>Double</td><td>Real</td><td>Chili</td><td>&nbsp;</td><td>77</td>
        </tr>

        <tr>
          <td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td>
        </tr>

        <tr>
          <td>Fortran90</td><td>Quad</td><td>Real</td><td>DHCP95 (Apple G5)</td><td>gfortran</td><td>23</td>
        </tr>
        <tr>
          <td>Fortran90</td><td>Quad</td><td>Real</td><td>Chili</td><td>&nbsp;</td><td>10</td>
        </tr>
      </table>
    </p>

    <h3 align = "center">
      Languages:
    </h3>

    <p>
      <b>LINPACK_BENCH</b> is available in
      <a href = "../../c_src/linpack_bench/linpack_bench.html">a C version</a> and
      <a href = "../../cpp_src/linpack_bench/linpack_bench.html">a C++ version</a> and
      <a href = "../../f77_src/linpack_bench/linpack_bench.html">a FORTRAN77 version</a> and
      <a href = "../../f_src/linpack_bench/linpack_bench.html">a FORTRAN90 version</a> and
      <a href = "../../j_src/linpack_bench/linpack_bench.html">a JAVA version</a> and
      <a href = "../../m_src/linpack_bench/linpack_bench.html">a MATLAB version</a>.
    </p>

    <h3 align = "center">
      Related Data and Programs:
    </h3>

    <p>
      <a href = "../../f_src/linpack_d/linpack_d.html">
      LINPACK_D</a>,
      a FORTRAN90 library which
      supplies the solvers used by <b>LINPACK_BENCH</b>.
    </p>

    <p>
      <a href = "../../f_src/matmul/matmul.html">
      MATMUL</a>,
      a FORTRAN90 program which
      is an interactive matrix multiplication benchmark program.
    </p>

    <p>
      <a href = "../../f77_src/mdbnch/mdbnch.html">
      MDBNCH</a>,
      a FORTRAN77 program which
      is a benchmark code for a molecular dynamics calculation.
    </p>

    <p>
      <a href = "../../f_src/memory_test/memory_test.html">
      MEMORY_TEST</a>,
      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.
    </p>

    <p>
      <a href = "../../f_src/mxm/mxm.html">
      MXM</a>,
      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.
    </p>

    <p>
      <a href = "../../f_src/mxv/mxv.html">
      MXV</a>,
      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.
    </p>

    <p>
      <a href = "../../f_src/nas/nas.html">
      NAS</a>,
      a FORTRAN90 program which
      runs the NASA kernel benchmark.
    </p>

    <p>
      <a href = "../../f_src/sum_million/sum_million.html">
      SUM_MILLION</a>,
      a FORTRAN90 program which
      sums the integers from 1 to 1,000,000, as a demonstration of how
      to rate a computer's speed;
    </p>

    <p>
      <a href = "../../f_src/timer/timer.html">
      TIMER</a>,
      a FORTRAN90 example which
      demonstrates how to measure CPU time or elapsed time.
    </p>

    <h3 align = "center">
      Reference:
    </h3>

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

    <h3 align = "center">
      Source Code:
    </h3>

    <p>
      <b>LINPACK_BENCH_S</b> is the single precision version:
      <ul>
        <li>
          <a href = "linpack_bench_s.f90">linpack_bench_s.f90</a>,
          the source code.
        </li>
        <li>
          <a href = "linpack_bench_s.sh">linpack_bench_s.sh</a>,
          commands to compile and load the source code.
        </li>
        <li>
          <a href = "linpack_bench_s.ll">linpack_bench_s.ll</a>,
          commands to compile and load the source code on a system
          that uses IBM's LoadLeveler batch queueing system.
        </li>
        <li>
          <a href = "linpack_bench_s_chili_output.txt">
          linpack_bench_s_chili_output.txt</a>,
          the output from an ALPHA named "Chili".
        </li>
        <li>
          <a href = "linpack_bench_s_dhcp95_output.txt">
          linpack_bench_s_dhcp95_output.txt</a>,
          the output from an Apple G5 named "DHCP95".
        </li>
        <li>
          <a href = "linpack_bench_s_eclipse_output.txt">
          linpack_bench_s_eclipse_output.txt</a>,
          the output from one (Power4) processor
          of ECLIPSE, an IBM pSeries 690.
        </li>
        <li>
          <a href = "linpack_bench_s_kachina_output.txt">
          linpack_bench_s_kachina_output.txt</a>,
          the output from  an ALPHA named "Kachina".
        </li>
        <li>
          <a href = "linpack_bench_s_sgi_output.txt">
          linpack_bench_s_sgi_output.txt</a>,
          the output from an SGI.
        </li>
        <li>
          <a href = "linpack_bench_s_teragold_output.txt">
          linpack_bench_s_teragold_output.txt</a>,
          the output from one (Power3) processor
          of TERAGOLD, an IBM pSeries 690.
        </li>
      </ul>
    </p>

    <p>
      <b>LINPACK_BENCH_D</b> is the double precision version:
      <ul>
        <li>
          <a href = "linpack_bench_d.f90">linpack_bench_d.f90</a>,
          the source code.
        </li>
        <li>
          <a href = "linpack_bench_d.sh">linpack_bench_d.sh</a>,
          commands to compile and load the source code.
        </li>
        <li>
          <a href = "linpack_bench_d_chili_output.txt">
          linpack_bench_d_chili_output.txt</a>,
          the output an ALPHA named "Chili".
        </li>
        <li>
          <a href = "linpack_bench_d_dhcp95_output.txt">
          linpack_bench_d_dhcp95_output.txt</a>,
          the output from an Apple G5 named "DHCP95".
        </li>
        <li>
          <a href = "linpack_bench_d_kachina_output.txt">
          linpack_bench_d_kachina_output.txt</a>,
          the output from an ALPHA named "Kachina".
        </li>
      </ul>
    </p>

    <p>
      <b>LINPACK_BENCH_Q</b> 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):
      <ul>
        <li>
          <a href = "linpack_bench_q.f90">linpack_bench_q.f90</a>,
          the source code.
        </li>
        <li>
          <a href = "linpack_bench_q.sh">linpack_bench_q.sh</a>,
          commands to compile and load the source code.
        </li>
        <li>
          <a href = "linpack_bench_q_chili_output.txt">
          linpack_bench_q_chili_output.txt</a>,
          the output from an ALPHA named "Chili".
        </li>
        <li>
          <a href = "linpack_bench_q_dhcp95_output.txt">
          linpack_bench_q_dhcp95_output.txt</a>,
          the output from an Apple G5 named "DHCP95".
        </li>
      </ul>
    </p>

    <h3 align = "center">
      List of Routines:
    </h3>

    <p>
      This is the list of routines for the double precision version of the
      benchmark program.  The single and quad precision names are similar.
      <ul>
        <li>
          <b>LINPACK_BENCH_D</b> drives the double precision LINPACK benchmark program.
        </li>
        <li>
          <b>D_MATGEN</b> generates a random matrix.
        </li>
        <li>
          <b>D_RANDOM</b> returns a uniformly distributed random number between 0 and 1.
        </li>
        <li>
          <b>DAXPY</b> adds a constant times one vector to another.
        </li>
        <li>
          <b>DGEFA</b> factors a real matrix.
        </li>
        <li>
          <b>DGESL</b> solves a real general linear system A * X = B.
        </li>
        <li>
          <b>IDAMAX</b> finds the index of the vector element of maximum absolute value.
        </li>
        <li>
          <b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
        </li>
      </ul>
    </p>

    <p>
      You can go up one level to <a href = "../f_src.html">
      the FORTRAN90 source codes</a>.
    </p>

    <hr>

    <i>
      Last revised on 07 March 2008.
    </i>

    <!-- John Burkardt -->

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