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