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cannam@127 3 <!-- This manual is for FFTW
cannam@127 4 (version 3.3.5, 30 July 2016).
cannam@127 5
cannam@127 6 Copyright (C) 2003 Matteo Frigo.
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cannam@127 8 Copyright (C) 2003 Massachusetts Institute of Technology.
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cannam@127 24 <head>
cannam@127 25 <title>FFTW 3.3.5: Introduction</title>
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cannam@127 70
cannam@127 71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
cannam@127 72 <a name="Introduction"></a>
cannam@127 73 <div class="header">
cannam@127 74 <p>
cannam@127 75 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@127 76 </div>
cannam@127 77 <hr>
cannam@127 78 <a name="Introduction-1"></a>
cannam@127 79 <h2 class="chapter">1 Introduction</h2>
cannam@127 80 <p>This manual documents version 3.3.5 of FFTW, the
cannam@127 81 <em>Fastest Fourier Transform in the West</em>. FFTW is a comprehensive
cannam@127 82 collection of fast C routines for computing the discrete Fourier
cannam@127 83 transform (DFT) and various special cases thereof.
cannam@127 84 <a name="index-discrete-Fourier-transform"></a>
cannam@127 85 <a name="index-DFT"></a>
cannam@127 86 </p><ul>
cannam@127 87 <li> FFTW computes the DFT of complex data, real data, even-
cannam@127 88 or odd-symmetric real data (these symmetric transforms are usually
cannam@127 89 known as the discrete cosine or sine transform, respectively), and the
cannam@127 90 discrete Hartley transform (DHT) of real data.
cannam@127 91
cannam@127 92 </li><li> The input data can have arbitrary length.
cannam@127 93 FFTW employs <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>) algorithms for all lengths, including
cannam@127 94 prime numbers.
cannam@127 95
cannam@127 96 </li><li> FFTW supports arbitrary multi-dimensional data.
cannam@127 97
cannam@127 98 </li><li> FFTW supports the SSE, SSE2, AVX, AVX2, AVX512, KCVI, Altivec, VSX, and
cannam@127 99 NEON vector instruction sets.
cannam@127 100
cannam@127 101 </li><li> FFTW includes parallel (multi-threaded) transforms
cannam@127 102 for shared-memory systems.
cannam@127 103 </li><li> Starting with version 3.3, FFTW includes distributed-memory parallel
cannam@127 104 transforms using MPI.
cannam@127 105 </li></ul>
cannam@127 106
cannam@127 107 <p>We assume herein that you are familiar with the properties and uses of
cannam@127 108 the DFT that are relevant to your application. Otherwise, see
cannam@127 109 e.g. <cite>The Fast Fourier Transform and Its Applications</cite> by E. O. Brigham
cannam@127 110 (Prentice-Hall, Englewood Cliffs, NJ, 1988).
cannam@127 111 <a href="http://www.fftw.org">Our web page</a> also has links to FFT-related
cannam@127 112 information online.
cannam@127 113 <a name="index-FFTW"></a>
cannam@127 114 </p>
cannam@127 115
cannam@127 116 <p>In order to use FFTW effectively, you need to learn one basic concept
cannam@127 117 of FFTW&rsquo;s internal structure: FFTW does not use a fixed algorithm for
cannam@127 118 computing the transform, but instead it adapts the DFT algorithm to
cannam@127 119 details of the underlying hardware in order to maximize performance.
cannam@127 120 Hence, the computation of the transform is split into two phases.
cannam@127 121 First, FFTW&rsquo;s <em>planner</em> &ldquo;learns&rdquo; the fastest way to compute the
cannam@127 122 transform on your machine. The planner
cannam@127 123 <a name="index-planner"></a>
cannam@127 124 produces a data structure called a <em>plan</em> that contains this
cannam@127 125 <a name="index-plan"></a>
cannam@127 126 information. Subsequently, the plan is <em>executed</em>
cannam@127 127 <a name="index-execute"></a>
cannam@127 128 to transform the array of input data as dictated by the plan. The
cannam@127 129 plan can be reused as many times as needed. In typical
cannam@127 130 high-performance applications, many transforms of the same size are
cannam@127 131 computed and, consequently, a relatively expensive initialization of
cannam@127 132 this sort is acceptable. On the other hand, if you need a single
cannam@127 133 transform of a given size, the one-time cost of the planner becomes
cannam@127 134 significant. For this case, FFTW provides fast planners based on
cannam@127 135 heuristics or on previously computed plans.
cannam@127 136 </p>
cannam@127 137 <p>FFTW supports transforms of data with arbitrary length, rank,
cannam@127 138 multiplicity, and a general memory layout. In simple cases, however,
cannam@127 139 this generality may be unnecessary and confusing. Consequently, we
cannam@127 140 organized the interface to FFTW into three levels of increasing
cannam@127 141 generality.
cannam@127 142 </p><ul>
cannam@127 143 <li> The <em>basic interface</em> computes a single
cannam@127 144 transform of contiguous data.
cannam@127 145 </li><li> The <em>advanced interface</em> computes transforms
cannam@127 146 of multiple or strided arrays.
cannam@127 147 </li><li> The <em>guru interface</em> supports the most general data
cannam@127 148 layouts, multiplicities, and strides.
cannam@127 149 </li></ul>
cannam@127 150 <p>We expect that most users will be best served by the basic interface,
cannam@127 151 whereas the guru interface requires careful attention to the
cannam@127 152 documentation to avoid problems.
cannam@127 153 <a name="index-basic-interface"></a>
cannam@127 154 <a name="index-advanced-interface"></a>
cannam@127 155 <a name="index-guru-interface"></a>
cannam@127 156 </p>
cannam@127 157
cannam@127 158 <p>Besides the automatic performance adaptation performed by the planner,
cannam@127 159 it is also possible for advanced users to customize FFTW manually. For
cannam@127 160 example, if code space is a concern, we provide a tool that links only
cannam@127 161 the subset of FFTW needed by your application. Conversely, you may need
cannam@127 162 to extend FFTW because the standard distribution is not sufficient for
cannam@127 163 your needs. For example, the standard FFTW distribution works most
cannam@127 164 efficiently for arrays whose size can be factored into small primes
cannam@127 165 (<em>2</em>, <em>3</em>, <em>5</em>, and <em>7</em>), and otherwise it uses a
cannam@127 166 slower general-purpose routine. If you need efficient transforms of
cannam@127 167 other sizes, you can use FFTW&rsquo;s code generator, which produces fast C
cannam@127 168 programs (&ldquo;codelets&rdquo;) for any particular array size you may care
cannam@127 169 about.
cannam@127 170 <a name="index-code-generator"></a>
cannam@127 171 <a name="index-codelet"></a>
cannam@127 172 For example, if you need transforms of size
cannam@127 173 513&nbsp;=&nbsp;19*3<sup>3</sup>,you can customize FFTW to support the factor <em>19</em> efficiently.
cannam@127 174 </p>
cannam@127 175 <p>For more information regarding FFTW, see the paper, &ldquo;The Design and
cannam@127 176 Implementation of FFTW3,&rdquo; by M. Frigo and S. G. Johnson, which was an
cannam@127 177 invited paper in <cite>Proc. IEEE</cite> <b>93</b> (2), p. 216 (2005). The
cannam@127 178 code generator is described in the paper &ldquo;A fast Fourier transform
cannam@127 179 compiler&rdquo;,
cannam@127 180 <a name="index-compiler"></a>
cannam@127 181 by M. Frigo, in the <cite>Proceedings of the 1999 ACM SIGPLAN Conference
cannam@127 182 on Programming Language Design and Implementation (PLDI), Atlanta,
cannam@127 183 Georgia, May 1999</cite>. These papers, along with the latest version of
cannam@127 184 FFTW, the FAQ, benchmarks, and other links, are available at
cannam@127 185 <a href="http://www.fftw.org">the FFTW home page</a>.
cannam@127 186 </p>
cannam@127 187 <p>The current version of FFTW incorporates many good ideas from the past
cannam@127 188 thirty years of FFT literature. In one way or another, FFTW uses the
cannam@127 189 Cooley-Tukey algorithm, the prime factor algorithm, Rader&rsquo;s algorithm
cannam@127 190 for prime sizes, and a split-radix algorithm (with a
cannam@127 191 &ldquo;conjugate-pair&rdquo; variation pointed out to us by Dan Bernstein).
cannam@127 192 FFTW&rsquo;s code generator also produces new algorithms that we do not
cannam@127 193 completely understand.
cannam@127 194 <a name="index-algorithm"></a>
cannam@127 195 The reader is referred to the cited papers for the appropriate
cannam@127 196 references.
cannam@127 197 </p>
cannam@127 198 <p>The rest of this manual is organized as follows. We first discuss the
cannam@127 199 sequential (single-processor) implementation. We start by describing
cannam@127 200 the basic interface/features of FFTW in <a href="Tutorial.html#Tutorial">Tutorial</a>.
cannam@127 201 Next, <a href="Other-Important-Topics.html#Other-Important-Topics">Other Important Topics</a> discusses data alignment
cannam@127 202 (see <a href="SIMD-alignment-and-fftw_005fmalloc.html#SIMD-alignment-and-fftw_005fmalloc">SIMD alignment and fftw_malloc</a>),
cannam@127 203 the storage scheme of multi-dimensional arrays
cannam@127 204 (see <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>), and FFTW&rsquo;s mechanism for
cannam@127 205 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@127 206 <a href="FFTW-Reference.html#FFTW-Reference">FFTW Reference</a> provides comprehensive documentation of all
cannam@127 207 FFTW&rsquo;s features. Parallel transforms are discussed in their own
cannam@127 208 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@127 209 <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@127 210 install FFTW in your computer system and how to adapt FFTW to your
cannam@127 211 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@127 212 <a href="Acknowledgments.html#Acknowledgments">Acknowledgments</a>.
cannam@127 213 </p>
cannam@127 214 <hr>
cannam@127 215 <div class="header">
cannam@127 216 <p>
cannam@127 217 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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