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<html>
<head>
<title>
FFT_OPENMP - Fast Fourier Transform Using OpenMP
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FFT_OPENMP <br> Fast Fourier Transform Using OpenMP
</h1>
<hr>
<p>
<b>FFT_OPENMP</b>
is a FORTRAN90 program which
demonstrates the computation of a Fast Fourier Transform
in parallel, using OpenMP.
</p>
<p>
On an Apple PowerPC G5 with two processors, the following results were
observed:
<table border="1" align="center">
<tr>
<th>Threads</th><th>N</th><th>Time</th><th>MegaFLOPS</th>
</tr>
<tr>
<td>1</td><td>33,554,432</td><td>35.44</td><td>118.4</td>
</tr>
<tr>
<td>2</td><td>33,554,432</td><td>20.58</td><td>203.8</td>
</tr>
<tr>
<td>4</td><td>33,554,432</td><td>20.79</td><td>201.7</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
./fft_openmp
</pre>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>FFT_OPENMP</b> is available in
<a href = "../../c_src/fft_openmp/fft_openmp.html">a C version</a> and
<a href = "../../cpp_src/fft_openmp/fft_openmp.html">a C++ version</a> and
<a href = "../../f77_src/fft_openmp/fft_openmp.html">a FORTRAN77 version</a> and
<a href = "../../f_src/fft_openmp/fft_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_serial/fft_serial.html">
FFT_SERIAL</a>,
a FORTRAN90 program which
demonstrates the computation of a Fast Fourier Transform,
and is intended as a starting point for implementing a parallel version
using OpenMP.
<p>
<p>
<a href = "../../f_src/fftpack5/fftpack5.html">
FFTPACK5</a>,
a FORTRAN90 library which
implements the Fast Fourier Transform
by Paul Swarztrauber and Dick Valent;
</p>
<p>
<a href = "../../f_src/fftpack5.1/fftpack5.1.html">
FFTPACK5.1</a>,
a FORTRAN90 library which
implements the Fast Fourier Transform
by Paul Swarztrauber and Dick Valent;
</p>
<p>
<a href = "../../f_src/fftw3/fftw3.html">
FFTW3</a>,
FORTRAN90 programs which
illustrate the use of the FFTW3 library for Fast Fourier Transforms,
by Matteo Frigo and Steven Johnson.
</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 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_openmp/prime_openmp.html">
PRIME_OPENMP</a>,
a FORTRAN90 program which
counts the number of primes between 1 and N, using OpenMP for parallel execution.
</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/sftpack/sftpack.html">
SFTPACK</a>,
a FORTRAN90 library which
implements the "slow" Fourier transform, intended as a teaching
tool and comparison with the fast Fourier transform.
</p>
<p>
<a href = "../../f_src/sgefa_openmp/sgefa_openmp.html">
SGEFA_OPENMP</a>,
a FORTRAN90 program which
solves a linear system by Gaussian elimination, using 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>
Wesley Petersen, Peter Arbenz, <br>
Introduction to Parallel Computing - A practical guide with examples in C,<br>
Oxford University Press,<br>
ISBN: 0-19-851576-6,<br>
LC: QA76.58.P47.
</li>
<li>
Rohit Chandra, Leonardo Dagum, Dave Kohr, Dror Maydan,
Jeff McDonald, Ramesh Menon,<br>
Parallel Programming in OpenMP,<br>
Morgan Kaufmann, 2001,<br>
ISBN: 1-55860-671-8,<br>
LC: QA76.642.P32.
</li>
<li>
Barbara Chapman, Gabriele Jost, Ruud vanderPas, David Kuck,<br>
Using OpenMP: Portable Shared Memory Parallel Processing,<br>
MIT Press, 2007,<br>
ISBN13: 978-0262533027,<br>
LC: QA76.642.C49.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "fft_openmp.f90">fft_openmp.f90</a>, the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>FFT_LOCAL_GFORTRAN</b> compiles, links, loads and runs the program
using 1, 2 and 4 threads, the local interactive environment,
and the GFORTRAN Fortran compiler.
<ul>
<li>
<a href = "fft_local_gfortran.sh">fft_local_gfortran.sh</a>,
BASH commands.
</li>
<li>
<a href = "fft_local_gfortran_output.txt">fft_local_gfortran_output.txt</a>,
the output file;
</li>
</ul>
</p>
<p>
<b>FFT_LOCAL_IFORT</b> compiles, links, loads and runs the program
using 1, 2 and 4 threads, the local interactive environment,
and the Intel IFORT Fortran compiler.
<ul>
<li>
<a href = "fft_local_ifort.sh">fft_local_ifort.sh</a>,
BASH commands.
</li>
<li>
<a href = "fft_local_ifort_output.txt">fft_local_ifort_output.txt</a>,
the output file;
</li>
</ul>
</p>
<p>
<b>FFT_ITHACA_GFORTRAN</b> compiles, links, loads and runs the program
using 1, 2 and 4 threads, using the PBS queueing system on Virginia
Tech's Ithaca cluster, and the GFORTRAN Fortran compiler.
<ul>
<li>
<a href = "fft_ithaca_gfortran.sh">fft_ithaca_gfortran.sh</a>,
BASH commands.
</li>
<li>
<a href = "fft_ithaca_gfortran_output.txt">fft_ithaca_gfortran_output.txt</a>,
the output file;
</li>
</ul>
</p>
<p>
<b>FFT_ITHACA_IFORT</b> compiles, links, loads and runs the program
using 1, 2 and 4 threads, using the PBS queueing system on Virginia
Tech's Ithaca cluster,
and the Intel IFORT Fortran compiler.
<ul>
<li>
<a href = "fft_ithaca_ifort.sh">fft_ithaca_ifort.sh</a>,
BASH commands.
</li>
<li>
<a href = "fft_ithaca_ifort_output.txt">fft_ithaca_ifort_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 FFT_OPENMP.
</li>
<li>
<b>CCOPY</b> copies a complex vector.
</li>
<li>
<b>CFFT2</b> performs a complex Fast Fourier Transform.
</li>
<li>
<b>CFFTI</b> sets up sine and cosine tables needed for the FFT calculation.
</li>
<li>
<b>GGL</b> generates u(0,1) distributed random numbers.
</li>
<li>
<b>STEP</b> carries out one step of the workspace version of CFFT2.
</li>
<li>
<b>TIMESTAMP</b> prints the YMDHMS date as a timestamp.
</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 19 May 2010.
</i>
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