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Add FFTW 3.3.8 source, and a Linux build
author Chris Cannam
date Tue, 19 Nov 2019 14:52:55 +0000
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Chris@82 3 <!-- This manual is for FFTW
Chris@82 4 (version 3.3.8, 24 May 2018).
Chris@82 5
Chris@82 6 Copyright (C) 2003 Matteo Frigo.
Chris@82 7
Chris@82 8 Copyright (C) 2003 Massachusetts Institute of Technology.
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Chris@82 11 manual provided the copyright notice and this permission notice are
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Chris@82 24 <head>
Chris@82 25 <title>FFTW 3.3.8: Introduction</title>
Chris@82 26
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Chris@82 68 </head>
Chris@82 69
Chris@82 70 <body lang="en">
Chris@82 71 <a name="Introduction"></a>
Chris@82 72 <div class="header">
Chris@82 73 <p>
Chris@82 74 Next: <a href="Tutorial.html#Tutorial" accesskey="n" rel="next">Tutorial</a>, Previous: <a href="index.html#Top" accesskey="p" rel="prev">Top</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
Chris@82 75 </div>
Chris@82 76 <hr>
Chris@82 77 <a name="Introduction-1"></a>
Chris@82 78 <h2 class="chapter">1 Introduction</h2>
Chris@82 79 <p>This manual documents version 3.3.8 of FFTW, the
Chris@82 80 <em>Fastest Fourier Transform in the West</em>. FFTW is a comprehensive
Chris@82 81 collection of fast C routines for computing the discrete Fourier
Chris@82 82 transform (DFT) and various special cases thereof.
Chris@82 83 <a name="index-discrete-Fourier-transform"></a>
Chris@82 84 <a name="index-DFT"></a>
Chris@82 85 </p><ul>
Chris@82 86 <li> FFTW computes the DFT of complex data, real data, even-
Chris@82 87 or odd-symmetric real data (these symmetric transforms are usually
Chris@82 88 known as the discrete cosine or sine transform, respectively), and the
Chris@82 89 discrete Hartley transform (DHT) of real data.
Chris@82 90
Chris@82 91 </li><li> The input data can have arbitrary length.
Chris@82 92 FFTW employs <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>)
Chris@82 93 algorithms for all lengths, including
Chris@82 94 prime numbers.
Chris@82 95
Chris@82 96 </li><li> FFTW supports arbitrary multi-dimensional data.
Chris@82 97
Chris@82 98 </li><li> FFTW supports the SSE, SSE2, AVX, AVX2, AVX512, KCVI, Altivec, VSX, and
Chris@82 99 NEON vector instruction sets.
Chris@82 100
Chris@82 101 </li><li> FFTW includes parallel (multi-threaded) transforms
Chris@82 102 for shared-memory systems.
Chris@82 103 </li><li> Starting with version 3.3, FFTW includes distributed-memory parallel
Chris@82 104 transforms using MPI.
Chris@82 105 </li></ul>
Chris@82 106
Chris@82 107 <p>We assume herein that you are familiar with the properties and uses of
Chris@82 108 the DFT that are relevant to your application. Otherwise, see
Chris@82 109 e.g. <cite>The Fast Fourier Transform and Its Applications</cite> by E. O. Brigham
Chris@82 110 (Prentice-Hall, Englewood Cliffs, NJ, 1988).
Chris@82 111 <a href="http://www.fftw.org">Our web page</a> also has links to FFT-related
Chris@82 112 information online.
Chris@82 113 <a name="index-FFTW"></a>
Chris@82 114 </p>
Chris@82 115
Chris@82 116 <p>In order to use FFTW effectively, you need to learn one basic concept
Chris@82 117 of FFTW&rsquo;s internal structure: FFTW does not use a fixed algorithm for
Chris@82 118 computing the transform, but instead it adapts the DFT algorithm to
Chris@82 119 details of the underlying hardware in order to maximize performance.
Chris@82 120 Hence, the computation of the transform is split into two phases.
Chris@82 121 First, FFTW&rsquo;s <em>planner</em> &ldquo;learns&rdquo; the fastest way to compute the
Chris@82 122 transform on your machine. The planner
Chris@82 123 <a name="index-planner"></a>
Chris@82 124 produces a data structure called a <em>plan</em> that contains this
Chris@82 125 <a name="index-plan"></a>
Chris@82 126 information. Subsequently, the plan is <em>executed</em>
Chris@82 127 <a name="index-execute"></a>
Chris@82 128 to transform the array of input data as dictated by the plan. The
Chris@82 129 plan can be reused as many times as needed. In typical
Chris@82 130 high-performance applications, many transforms of the same size are
Chris@82 131 computed and, consequently, a relatively expensive initialization of
Chris@82 132 this sort is acceptable. On the other hand, if you need a single
Chris@82 133 transform of a given size, the one-time cost of the planner becomes
Chris@82 134 significant. For this case, FFTW provides fast planners based on
Chris@82 135 heuristics or on previously computed plans.
Chris@82 136 </p>
Chris@82 137 <p>FFTW supports transforms of data with arbitrary length, rank,
Chris@82 138 multiplicity, and a general memory layout. In simple cases, however,
Chris@82 139 this generality may be unnecessary and confusing. Consequently, we
Chris@82 140 organized the interface to FFTW into three levels of increasing
Chris@82 141 generality.
Chris@82 142 </p><ul>
Chris@82 143 <li> The <em>basic interface</em> computes a single
Chris@82 144 transform of contiguous data.
Chris@82 145 </li><li> The <em>advanced interface</em> computes transforms
Chris@82 146 of multiple or strided arrays.
Chris@82 147 </li><li> The <em>guru interface</em> supports the most general data
Chris@82 148 layouts, multiplicities, and strides.
Chris@82 149 </li></ul>
Chris@82 150 <p>We expect that most users will be best served by the basic interface,
Chris@82 151 whereas the guru interface requires careful attention to the
Chris@82 152 documentation to avoid problems.
Chris@82 153 <a name="index-basic-interface"></a>
Chris@82 154 <a name="index-advanced-interface"></a>
Chris@82 155 <a name="index-guru-interface"></a>
Chris@82 156 </p>
Chris@82 157
Chris@82 158 <p>Besides the automatic performance adaptation performed by the planner,
Chris@82 159 it is also possible for advanced users to customize FFTW manually. For
Chris@82 160 example, if code space is a concern, we provide a tool that links only
Chris@82 161 the subset of FFTW needed by your application. Conversely, you may need
Chris@82 162 to extend FFTW because the standard distribution is not sufficient for
Chris@82 163 your needs. For example, the standard FFTW distribution works most
Chris@82 164 efficiently for arrays whose size can be factored into small primes
Chris@82 165 (<em>2</em>, <em>3</em>, <em>5</em>, and <em>7</em>), and otherwise it uses a
Chris@82 166 slower general-purpose routine. If you need efficient transforms of
Chris@82 167 other sizes, you can use FFTW&rsquo;s code generator, which produces fast C
Chris@82 168 programs (&ldquo;codelets&rdquo;) for any particular array size you may care
Chris@82 169 about.
Chris@82 170 <a name="index-code-generator"></a>
Chris@82 171 <a name="index-codelet"></a>
Chris@82 172 For example, if you need transforms of size
Chris@82 173 513&nbsp;=&nbsp;19*3<sup>3</sup>,
Chris@82 174 you can customize FFTW to support the factor <em>19</em> efficiently.
Chris@82 175 </p>
Chris@82 176 <p>For more information regarding FFTW, see the paper, &ldquo;The Design and
Chris@82 177 Implementation of FFTW3,&rdquo; by M. Frigo and S. G. Johnson, which was an
Chris@82 178 invited paper in <cite>Proc. IEEE</cite> <b>93</b> (2), p. 216 (2005). The
Chris@82 179 code generator is described in the paper &ldquo;A fast Fourier transform
Chris@82 180 compiler&rdquo;,
Chris@82 181 <a name="index-compiler"></a>
Chris@82 182 by M. Frigo, in the <cite>Proceedings of the 1999 ACM SIGPLAN Conference
Chris@82 183 on Programming Language Design and Implementation (PLDI), Atlanta,
Chris@82 184 Georgia, May 1999</cite>. These papers, along with the latest version of
Chris@82 185 FFTW, the FAQ, benchmarks, and other links, are available at
Chris@82 186 <a href="http://www.fftw.org">the FFTW home page</a>.
Chris@82 187 </p>
Chris@82 188 <p>The current version of FFTW incorporates many good ideas from the past
Chris@82 189 thirty years of FFT literature. In one way or another, FFTW uses the
Chris@82 190 Cooley-Tukey algorithm, the prime factor algorithm, Rader&rsquo;s algorithm
Chris@82 191 for prime sizes, and a split-radix algorithm (with a
Chris@82 192 &ldquo;conjugate-pair&rdquo; variation pointed out to us by Dan Bernstein).
Chris@82 193 FFTW&rsquo;s code generator also produces new algorithms that we do not
Chris@82 194 completely understand.
Chris@82 195 <a name="index-algorithm"></a>
Chris@82 196 The reader is referred to the cited papers for the appropriate
Chris@82 197 references.
Chris@82 198 </p>
Chris@82 199 <p>The rest of this manual is organized as follows. We first discuss the
Chris@82 200 sequential (single-processor) implementation. We start by describing
Chris@82 201 the basic interface/features of FFTW in <a href="Tutorial.html#Tutorial">Tutorial</a>.
Chris@82 202 Next, <a href="Other-Important-Topics.html#Other-Important-Topics">Other Important Topics</a> discusses data alignment
Chris@82 203 (see <a href="SIMD-alignment-and-fftw_005fmalloc.html#SIMD-alignment-and-fftw_005fmalloc">SIMD alignment and fftw_malloc</a>),
Chris@82 204 the storage scheme of multi-dimensional arrays
Chris@82 205 (see <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>), and FFTW&rsquo;s mechanism for
Chris@82 206 storing plans on disk (see <a href="Words-of-Wisdom_002dSaving-Plans.html#Words-of-Wisdom_002dSaving-Plans">Words of Wisdom-Saving Plans</a>). Next,
Chris@82 207 <a href="FFTW-Reference.html#FFTW-Reference">FFTW Reference</a> provides comprehensive documentation of all
Chris@82 208 FFTW&rsquo;s features. Parallel transforms are discussed in their own
Chris@82 209 chapters: <a href="Multi_002dthreaded-FFTW.html#Multi_002dthreaded-FFTW">Multi-threaded FFTW</a> and <a href="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI">Distributed-memory FFTW with MPI</a>. Fortran programmers can also use FFTW, as described in
Chris@82 210 <a href="Calling-FFTW-from-Legacy-Fortran.html#Calling-FFTW-from-Legacy-Fortran">Calling FFTW from Legacy Fortran</a> and <a href="Calling-FFTW-from-Modern-Fortran.html#Calling-FFTW-from-Modern-Fortran">Calling FFTW from Modern Fortran</a>. <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a> explains how to
Chris@82 211 install FFTW in your computer system and how to adapt FFTW to your
Chris@82 212 needs. License and copyright information is given in <a href="License-and-Copyright.html#License-and-Copyright">License and Copyright</a>. Finally, we thank all the people who helped us in
Chris@82 213 <a href="Acknowledgments.html#Acknowledgments">Acknowledgments</a>.
Chris@82 214 </p>
Chris@82 215 <hr>
Chris@82 216 <div class="header">
Chris@82 217 <p>
Chris@82 218 Next: <a href="Tutorial.html#Tutorial" accesskey="n" rel="next">Tutorial</a>, Previous: <a href="index.html#Top" accesskey="p" rel="prev">Top</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
Chris@82 219 </div>
Chris@82 220
Chris@82 221
Chris@82 222
Chris@82 223 </body>
Chris@82 224 </html>