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<html>
<head>
<title>
FFT_SERIAL - Fast Fourier Transform
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FFT_SERIAL <br> Fast Fourier Transform
</h1>
<hr>
<p>
<b>FFT_SERIAL</b>
is a C++ program which
demonstrates the computation of a Fast Fourier Transform,
and is intended as a starting point for developing a parallel version
using OpenMP.
</p>
<p>
On an Apple PowerPC G5 with two processors, the following results were
observed:
<table border="1" align="center">
<tr>
<th>N</th><th>Time</th><th>MegaFLOPS</th>
</tr>
<tr><td> 2</td><td>4.3525e-07</td><td> 22.9753</td></tr>
<tr><td> 4</td><td>1.15245e-06</td><td> 34.7087</td></tr>
<tr><td> 8</td><td>2.20385e-06</td><td> 54.4502</td></tr>
<tr><td> 16</td><td>4.509e-06</td><td> 70.9692</td></tr>
<tr><td> 32</td><td>6.798e-06</td><td> 117.682</td></tr>
<tr><td> 64</td><td>1.61065e-05</td><td> 119.207</td></tr>
<tr><td> 128</td><td>3.28125e-05</td><td> 136.533</td></tr>
<tr><td> 256</td><td>7.6573e-05</td><td> 133.729</td></tr>
<tr><td> 512</td><td>0.000157155</td><td> 146.607</td></tr>
<tr><td> 1024</td><td>0.00035841</td><td> 142.853</td></tr>
<tr><td> 2048</td><td>0.00075819</td><td> 148.564</td></tr>
<tr><td> 4096</td><td>0.00170309</td><td> 144.302</td></tr>
<tr><td> 8192</td><td>0.00348095</td><td> 152.970</td></tr>
<tr><td> 16384</td><td>0.00811195</td><td> 141.382</td></tr>
<tr><td> 32768</td><td>0.0173951</td><td> 141.281</td></tr>
<tr><td> 65536</td><td>0.0402766</td><td> 130.172</td></tr>
<tr><td> 131072</td><td>0.083454</td><td> 133.500</td></tr>
<tr><td> 262144</td><td>0.184454</td><td> 127.907</td></tr>
<tr><td> 524288</td><td>0.382927</td><td> 130.070</td></tr>
<tr><td>1048576</td><td>0.835447</td><td> 125.511</td></tr>
</table>
</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>FFT_SERIAL</b> is available in
<a href = "../../c_src/fft_serial/fft_serial.html">a C version</a> and
<a href = "../../cpp_src/fft_serial/fft_serial.html">a C++ version</a> and
<a href = "../../f77_src/fft_serial/fft_serial.html">a FORTRAN77 version</a> and
<a href = "../../f_src/fft_serial/fft_serial.html">a FORTRAN90 version</a> and
<a href = "../../m_src/fft_serial/fft_serial.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/fft_openmp/fft_openmp.html">
FFT_OPENMP</a>,
a C++ program which
computes a Fast Fourier Transform using OpenMP.
<p>
<p>
<a href = "../../cpp_src/fire_serial/fire_serial.html">
FIRE_SERIAL</a>,
a C++ program which
simulates a forest fire over a rectangular array of trees,
starting at a single random location. It is intended as a starting
point for the development of a parallel version.
</p>
<p>
<a href = "../../cpp_src/heated_plate/heated_plate.html">
HEATED_PLATE</a>,
a C++ program which
solves the steady state heat equation in a 2D
rectangular region, and is intended as
a starting point for implementing an OpenMP parallel version.
</p>
<p>
<a href = "../../cpp_src/md/md.html">
MD</a>,
a C++ program which
carries out a molecular dynamics simulation,
and is intended as a starting point for developing a parallel version
using OpenMP.
<p>
<p>
<a href = "../../cpp_src/mxm_serial/mxm_serial.html">
MXM_SERIAL</a>,
a C++ program which
sets up a matrix multiplication problem A=B*C,
intended as a starting point for implementing a parallel version.
</p>
<p>
<a href = "../../cpp_src/openmp/openmp.html">
OPENMP</a>,
C++ 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 = "../../cpp_src/poisson_serial/poisson_serial.html">
POISSON_SERIAL</a>,
a C++ program which
computes an approximate solution to the Poisson equation in a rectangle,
and is intended as the starting point for the creation of a parallel version.
</p>
<p>
<a href = "../../cpp_src/prime_serial/prime_serial.html">
PRIME_SERIAL</a>,
a C++ 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 = "../../cpp_src/quad_serial/quad_serial.html">
QUAD_SERIAL</a>,
a C++ program which
approximates an integral using a quadrature rule,
and is intended as a starting point for parallelization exercises.
</p>
<p>
<a href = "../../cpp_src/search_serial/search_serial.html">
SEARCH_SERIAL</a>,
a C++ program which
searches the integers from A to B for a value J such that F(J) = C.
this version of the program is intended as a starting point for
a parallel approach.
</p>
<p>
<a href = "../../cpp_src/sftpack/sftpack.html">
SFTPACK</a>,
a C++ library which
implements the "slow" Fourier transform, intended as a teaching
tool and comparison with the fast Fourier transform.
</p>
<p>
<a href = "../../cpp_src/sine_transform/sine_transform.html">
SINE_TRANSFORM</a>,
a C++ library which
demonstrates some simple properties of the discrete sine transform.
</p>
<p>
<a href = "../../cpp_src/subset_sum_serial/subset_sum_serial.html">
SUBSET_SUM_SERIAL</a>,
a C++ program which
seeks solutions of the subset sum problem, in which it is desired
to find a subset of a set of integers which has a given sum;
this version of the program is intended as a starting point for
a parallel approach.
</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_serial.cpp">fft_serial.cpp</a>, the source code.
</li>
<li>
<a href = "fft_serial.sh">fft_serial.sh</a>,
commands to compile, link and load the program.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "fft_serial_output.txt">fft_serial_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.
</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>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 23 March 2009.
</i>
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