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<html>
<head>
<title>
PRIME_OPENMP - Count Primes Using OpenMP
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
PRIME_OPENMP <br> Count Primes Using OpenMP
</h1>
<hr>
<p>
<b>PRIME_OPENMP</b>
is a FORTRAN90 program which
counts the number of primes between 1 and N,
using OpenMP to carry out the calculation in parallel.
</p>
<p>
The algorithm is completely naive. For each integer I, it simply checks
whether any smaller J evenly divides it. The total amount of work
for a given N is thus roughly proportional to 1/2*N^2.
</p>
<p>
This program is mainly a starting point for investigations into
parallelization.
</p>
<p>
Here are the counts of the number of primes for some selected values of N:
<table border="1" align="center">
<tr>
<th>N</th><th>Pi(N), Number of Primes</th>
</tr>
<tr><td> 1</td><td> 0</td></tr>
<tr><td> 2</td><td> 1</td></tr>
<tr><td> 4 </td><td> 2</td></tr>
<tr><td> 8</td><td> 4</td></tr>
<tr><td> 16</td><td> 6</td></tr>
<tr><td> 32</td><td> 11</td></tr>
<tr><td> 64</td><td> 18</td></tr>
<tr><td> 128</td><td> 31</td></tr>
<tr><td> 256</td><td> 54</td></tr>
<tr><td> 512</td><td> 97</td></tr>
<tr><td> 1024</td><td> 172</td></tr>
<tr><td> 2048</td><td> 309</td></tr>
<tr><td> 4096</td><td> 564</td></tr>
<tr><td> 8192</td><td> 1028</td></tr>
<tr><td> 16384</td><td> 1900</td></tr>
<tr><td> 32768</td><td> 3512 </td></tr>
<tr><td> 65536</td><td> 6542</td></tr>
<tr><td> 131072</td><td> 12251</td></tr>
</table>
</p>
<p>
The following results were observed for the elapsed time on a machine
that had 2 cores:
<table border="1" align="center">
<tr>
<th>N</th><th>Pi(N)</th><th>Time (1 Thread)</th><th>Time (2 Threads)</th><th>Time (4 Threads)</th>
</tr>
<tr><td> 16384</td><td> 1900</td><td> 0.377</td><td> 0.293</td><td> 0.220</td></tr>
<tr><td> 32768</td><td> 3512</td><td> 1.392</td><td> 1.061</td><td> 0.824</td></tr>
<tr><td> 65536</td><td> 6542</td><td> 5.221</td><td> 3.883</td><td> 3.012</td></tr>
<tr><td> 131072</td><td> 12251</td><td> 19.727</td><td>14.592</td><td>11.672</td></tr>
</table>
</p>
<h3 align = "center">
Usage:
</h3>
<p>
In the BASH shell, the program could be run with 2 threads using the commands:
<pre>
export OMP_NUM_THREADS=2
./prime_openmp
</pre>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>PRIME_OPENMP</b> is available in
<a href = "../../c_src/prime_openmp/prime_openmp.html">a C version</a> and
<a href = "../../cpp_src/prime_openmp/prime_openmp.html">a C++ version</a> and
<a href = "../../f77_src/prime_openmp/prime_openmp.html">a FORTRAN77 version</a> and
<a href = "../../f_src/prime_openmp/prime_openmp.html">a FORTRAN90 version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/dijkstra_openmp/dijkstra_openmp.html">
DIJKSTRA_OPENMP</a>,
a FORTRAN90 program which
uses OpenMP to parallelize a simple example of Dijkstra's
minimum distance algorithm for graphs.
</p>
<p>
<a href = "../../f_src/fft_openmp/fft_openmp.html">
FFT_OPENMP</a>,
a FORTRAN90 program which
demonstrates the computation of a Fast Fourier Transform
in parallel, using OpenMP.
</p>
<p>
<a href = "../../f_src/heated_plate_openmp/heated_plate_openmp.html">
HEATED_PLATE_OPENMP</a>,
a FORTRAN90 program which
solves the steady (time independent) heat equation in a 2D
rectangular region, using OpenMP to run in parallel.
</p>
<p>
<a href = "../../f_src/hello_openmp/hello_openmp.html">
HELLO_OPENMP</a>,
a FORTRAN90 program which
prints out "Hello, world!" using the OpenMP parallel programming environment.
</p>
<p>
<a href = "../../f_src/mandelbrot_openmp/mandelbrot_openmp.html">
MANDELBROT_OPENMP</a>,
a FORTRAN90 program which
generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set,
using OpenMP for parallel execution.
</p>
<p>
<a href = "../../f_src/md_openmp/md_openmp.html">
MD_OPENMP</a>,
a FORTRAN90 program which
carries out a molecular dynamics simulation in parallel,
using OpenMP.
<p>
<p>
<a href = "../../f_src/multitask_openmp/multitask_openmp.html">
MULTITASK_OPENMP</a>,
a FORTRAN90 program which
demonstrates how to "multitask", that is, to execute several unrelated
and distinct tasks simultaneously, using OpenMP for parallel execution.
</p>
<p>
<a href = "../../f_src/mxv_openmp/mxv_openmp.html">
MXM_OPENMP</a>,
a FORTRAN90 program which
computes a dense matrix product C=A*B,
using OpenMP for parallel execution.
<p>
<p>
<a href = "../../f_src/mxv_openmp/mxv_openmp.html">
MXV_OPENMP</a>,
a FORTRAN90 program which
compares the performance of plain vanilla Fortran and the FORTRAN90
intrinsic routine MATMUL, for the matrix multiplication problem
y=A*x, with and without parallelization by OpenMP.
<p>
<p>
<a href = "../../f_src/openmp/openmp.html">
OPENMP</a>,
FORTRAN90 programs which
illustrate the use of the OpenMP application program interface
for carrying out parallel computations in a shared memory environment.
</p>
<p>
<a href = "../../f_src/poisson_openmp/poisson_openmp.html">
POISSON_OPENMP</a>,
a FORTRAN90 program which
computes an approximate solution to the Poisson equation in a rectangle,
using the Jacobi iteration to solve the linear system, and OpenMP to
carry out the Jacobi iteration in parallel.
</p>
<p>
<a href = "../../f_src/prime_mpi/prime_mpi.html">
PRIME_MPI</a>,
a FORTRAN90 program which
counts the number of primes between 1 and N, using MPI for parallel execution.
</p>
<p>
<a href = "../../m_src/prime_parfor/prime_parfor.html">
PRIME_PARFOR</a>,
a MATLAB program which
counts the number of primes between 1 and N; it runs in parallel
using MATLAB's "parfor" facility.
</p>
<p>
<a href = "../../f_src/prime_serial/prime_serial.html">
PRIME_SERIAL</a>,
a FORTRAN90 program which
counts the number of primes between 1 and N,
intended as a starting point for the creation of a parallel version.
</p>
<p>
<a href = "../../f_src/quad_openmp/quad_openmp.html">
QUAD_OPENMP</a>,
a FORTRAN90 program which
approximates an integral using a quadrature rule, and carries out the
computation in parallel using OpenMP.
</p>
<p>
<a href = "../../f_src/random_openmp/random_openmp.html">
RANDOM_OPENMP</a>,
a FORTRAN90 program which
illustrates how a parallel program using OpenMP can generate multiple
distinct streams of random numbers.
</p>
<p>
<a href = "../../f_src/satisfy_openmp/satisfy_openmp.html">
SATISFY_OPENMP</a>,
a FORTRAN90 program which
demonstrates, for a particular circuit, an exhaustive search
for solutions of the circuit satisfiability problem,
using OpenMP for parallel execution.
<p>
<p>
<a href = "../../f_src/schedule_openmp/schedule_openmp.html">
SCHEDULE_OPENMP</a>,
a FORTRAN90 program which
demonstrates the default, static, and dynamic methods of "scheduling"
loop iterations in OpenMP to avoid work imbalance.
<p>
<p>
<a href = "../../f_src/sgefa_openmp/sgefa_openmp.html">
SGEFA_OPENMP</a>,
a FORTRAN90 program which
reimplements the SGEFA/SGESL linear algebra routines from
LINPACK for use with OpenMP.
</p>
<p>
<a href = "../../f_src/ziggurat_openmp/ziggurat_openmp.html">
ZIGGURAT_OPENMP</a>,
a FORTRAN90 program which
demonstrates how the ZIGGURAT library can be used to generate random numbers
in an OpenMP parallel program.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Eratosthenes,<br>
A Method For Finding Prime Numbers,<br>
Papyrus 487.
</li>
<li>
Michael Quinn,<br>
Parallel Programming in C with MPI and OpenMP,<br>
McGraw-Hill, 2004,<br>
ISBN13: 978-0071232654,<br>
LC: QA76.73.C15.Q55.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "prime_openmp.f90">prime_openmp.f90</a>, the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>PRIME_LOCAL</b> runs the program locally.
<ul>
<li>
<a href = "prime_local.sh">prime_local.sh</a>,
commands to compile the program and run with 1, 2, 4, and 8 threads.
</li>
<li>
<a href = "prime_local_output.txt">prime_local_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
<b>PRIME_ITHACA</b> runs the program through ITHACA's batch system.
<ul>
<li>
<a href = "prime_ithaca.sh">prime_ithaca.sh</a>,
commands to compile the program and run with 1, 2, 4, and 8 threads.
</li>
<li>
<a href = "prime_ithaca_output.txt">prime_ithaca_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for PRIME_OPENMP.
</li>
<li>
<b>PRIME_NUMBER</b> returns the number of primes between 1 and N.
</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 03 September 2009.
</i>
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