Mercurial > hg > sv-dependency-builds

annotate src/fftw-3.3.5/doc/html/Introduction.html @ 42:2cd0e3b3e1fd

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Current fftw source
author Chris Cannam
date Tue, 18 Oct 2016 13:40:26 +0100
parents
children
rev   line source
Chris@42 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
Chris@42 2 <html>
Chris@42 3 <!-- This manual is for FFTW
Chris@42 4 (version 3.3.5, 30 July 2016).
Chris@42 5
Chris@42 6 Copyright (C) 2003 Matteo Frigo.
Chris@42 7
Chris@42 8 Copyright (C) 2003 Massachusetts Institute of Technology.
Chris@42 9
Chris@42 10 Permission is granted to make and distribute verbatim copies of this
Chris@42 11 manual provided the copyright notice and this permission notice are
Chris@42 12 preserved on all copies.
Chris@42 13
Chris@42 14 Permission is granted to copy and distribute modified versions of this
Chris@42 15 manual under the conditions for verbatim copying, provided that the
Chris@42 16 entire resulting derived work is distributed under the terms of a
Chris@42 17 permission notice identical to this one.
Chris@42 18
Chris@42 19 Permission is granted to copy and distribute translations of this manual
Chris@42 20 into another language, under the above conditions for modified versions,
Chris@42 21 except that this permission notice may be stated in a translation
Chris@42 22 approved by the Free Software Foundation. -->
Chris@42 23 <!-- Created by GNU Texinfo 5.2, http://www.gnu.org/software/texinfo/ -->
Chris@42 24 <head>
Chris@42 25 <title>FFTW 3.3.5: Introduction</title>
Chris@42 26
Chris@42 27 <meta name="description" content="FFTW 3.3.5: Introduction">
Chris@42 28 <meta name="keywords" content="FFTW 3.3.5: Introduction">
Chris@42 29 <meta name="resource-type" content="document">
Chris@42 30 <meta name="distribution" content="global">
Chris@42 31 <meta name="Generator" content="makeinfo">
Chris@42 32 <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
Chris@42 33 <link href="index.html#Top" rel="start" title="Top">
Chris@42 34 <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
Chris@42 35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
Chris@42 36 <link href="index.html#Top" rel="up" title="Top">
Chris@42 37 <link href="Tutorial.html#Tutorial" rel="next" title="Tutorial">
Chris@42 38 <link href="index.html#Top" rel="prev" title="Top">
Chris@42 39 <style type="text/css">
Chris@42 40 <!--
Chris@42 41 a.summary-letter {text-decoration: none}
Chris@42 42 blockquote.smallquotation {font-size: smaller}
Chris@42 43 div.display {margin-left: 3.2em}
Chris@42 44 div.example {margin-left: 3.2em}
Chris@42 45 div.indentedblock {margin-left: 3.2em}
Chris@42 46 div.lisp {margin-left: 3.2em}
Chris@42 47 div.smalldisplay {margin-left: 3.2em}
Chris@42 48 div.smallexample {margin-left: 3.2em}
Chris@42 49 div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
Chris@42 50 div.smalllisp {margin-left: 3.2em}
Chris@42 51 kbd {font-style:oblique}
Chris@42 52 pre.display {font-family: inherit}
Chris@42 53 pre.format {font-family: inherit}
Chris@42 54 pre.menu-comment {font-family: serif}
Chris@42 55 pre.menu-preformatted {font-family: serif}
Chris@42 56 pre.smalldisplay {font-family: inherit; font-size: smaller}
Chris@42 57 pre.smallexample {font-size: smaller}
Chris@42 58 pre.smallformat {font-family: inherit; font-size: smaller}
Chris@42 59 pre.smalllisp {font-size: smaller}
Chris@42 60 span.nocodebreak {white-space:nowrap}
Chris@42 61 span.nolinebreak {white-space:nowrap}
Chris@42 62 span.roman {font-family:serif; font-weight:normal}
Chris@42 63 span.sansserif {font-family:sans-serif; font-weight:normal}
Chris@42 64 ul.no-bullet {list-style: none}
Chris@42 65 -->
Chris@42 66 </style>
Chris@42 67
Chris@42 68
Chris@42 69 </head>
Chris@42 70
Chris@42 71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
Chris@42 72 <a name="Introduction"></a>
Chris@42 73 <div class="header">
Chris@42 74 <p>
Chris@42 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>
Chris@42 76 </div>
Chris@42 77 <hr>
Chris@42 78 <a name="Introduction-1"></a>
Chris@42 79 <h2 class="chapter">1 Introduction</h2>
Chris@42 80 <p>This manual documents version 3.3.5 of FFTW, the
Chris@42 81 <em>Fastest Fourier Transform in the West</em>. FFTW is a comprehensive
Chris@42 82 collection of fast C routines for computing the discrete Fourier
Chris@42 83 transform (DFT) and various special cases thereof.
Chris@42 84 <a name="index-discrete-Fourier-transform"></a>
Chris@42 85 <a name="index-DFT"></a>
Chris@42 86 </p><ul>
Chris@42 87 <li> FFTW computes the DFT of complex data, real data, even-
Chris@42 88 or odd-symmetric real data (these symmetric transforms are usually
Chris@42 89 known as the discrete cosine or sine transform, respectively), and the
Chris@42 90 discrete Hartley transform (DHT) of real data.
Chris@42 91
Chris@42 92 </li><li> The input data can have arbitrary length.
Chris@42 93 FFTW employs <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>) algorithms for all lengths, including
Chris@42 94 prime numbers.
Chris@42 95
Chris@42 96 </li><li> FFTW supports arbitrary multi-dimensional data.
Chris@42 97
Chris@42 98 </li><li> FFTW supports the SSE, SSE2, AVX, AVX2, AVX512, KCVI, Altivec, VSX, and
Chris@42 99 NEON vector instruction sets.
Chris@42 100
Chris@42 101 </li><li> FFTW includes parallel (multi-threaded) transforms
Chris@42 102 for shared-memory systems.
Chris@42 103 </li><li> Starting with version 3.3, FFTW includes distributed-memory parallel
Chris@42 104 transforms using MPI.
Chris@42 105 </li></ul>
Chris@42 106
Chris@42 107 <p>We assume herein that you are familiar with the properties and uses of
Chris@42 108 the DFT that are relevant to your application. Otherwise, see
Chris@42 109 e.g. <cite>The Fast Fourier Transform and Its Applications</cite> by E. O. Brigham
Chris@42 110 (Prentice-Hall, Englewood Cliffs, NJ, 1988).
Chris@42 111 <a href="http://www.fftw.org">Our web page</a> also has links to FFT-related
Chris@42 112 information online.
Chris@42 113 <a name="index-FFTW"></a>
Chris@42 114 </p>
Chris@42 115
Chris@42 116 <p>In order to use FFTW effectively, you need to learn one basic concept
Chris@42 117 of FFTW&rsquo;s internal structure: FFTW does not use a fixed algorithm for
Chris@42 118 computing the transform, but instead it adapts the DFT algorithm to
Chris@42 119 details of the underlying hardware in order to maximize performance.
Chris@42 120 Hence, the computation of the transform is split into two phases.
Chris@42 121 First, FFTW&rsquo;s <em>planner</em> &ldquo;learns&rdquo; the fastest way to compute the
Chris@42 122 transform on your machine. The planner
Chris@42 123 <a name="index-planner"></a>
Chris@42 124 produces a data structure called a <em>plan</em> that contains this
Chris@42 125 <a name="index-plan"></a>
Chris@42 126 information. Subsequently, the plan is <em>executed</em>
Chris@42 127 <a name="index-execute"></a>
Chris@42 128 to transform the array of input data as dictated by the plan. The
Chris@42 129 plan can be reused as many times as needed. In typical
Chris@42 130 high-performance applications, many transforms of the same size are
Chris@42 131 computed and, consequently, a relatively expensive initialization of
Chris@42 132 this sort is acceptable. On the other hand, if you need a single
Chris@42 133 transform of a given size, the one-time cost of the planner becomes
Chris@42 134 significant. For this case, FFTW provides fast planners based on
Chris@42 135 heuristics or on previously computed plans.
Chris@42 136 </p>
Chris@42 137 <p>FFTW supports transforms of data with arbitrary length, rank,
Chris@42 138 multiplicity, and a general memory layout. In simple cases, however,
Chris@42 139 this generality may be unnecessary and confusing. Consequently, we
Chris@42 140 organized the interface to FFTW into three levels of increasing
Chris@42 141 generality.
Chris@42 142 </p><ul>
Chris@42 143 <li> The <em>basic interface</em> computes a single
Chris@42 144 transform of contiguous data.
Chris@42 145 </li><li> The <em>advanced interface</em> computes transforms
Chris@42 146 of multiple or strided arrays.
Chris@42 147 </li><li> The <em>guru interface</em> supports the most general data
Chris@42 148 layouts, multiplicities, and strides.
Chris@42 149 </li></ul>
Chris@42 150 <p>We expect that most users will be best served by the basic interface,
Chris@42 151 whereas the guru interface requires careful attention to the
Chris@42 152 documentation to avoid problems.
Chris@42 153 <a name="index-basic-interface"></a>
Chris@42 154 <a name="index-advanced-interface"></a>
Chris@42 155 <a name="index-guru-interface"></a>
Chris@42 156 </p>
Chris@42 157
Chris@42 158 <p>Besides the automatic performance adaptation performed by the planner,
Chris@42 159 it is also possible for advanced users to customize FFTW manually. For
Chris@42 160 example, if code space is a concern, we provide a tool that links only
Chris@42 161 the subset of FFTW needed by your application. Conversely, you may need
Chris@42 162 to extend FFTW because the standard distribution is not sufficient for
Chris@42 163 your needs. For example, the standard FFTW distribution works most
Chris@42 164 efficiently for arrays whose size can be factored into small primes
Chris@42 165 (<em>2</em>, <em>3</em>, <em>5</em>, and <em>7</em>), and otherwise it uses a
Chris@42 166 slower general-purpose routine. If you need efficient transforms of
Chris@42 167 other sizes, you can use FFTW&rsquo;s code generator, which produces fast C
Chris@42 168 programs (&ldquo;codelets&rdquo;) for any particular array size you may care
Chris@42 169 about.
Chris@42 170 <a name="index-code-generator"></a>
Chris@42 171 <a name="index-codelet"></a>
Chris@42 172 For example, if you need transforms of size
Chris@42 173 513&nbsp;=&nbsp;19*3<sup>3</sup>,you can customize FFTW to support the factor <em>19</em> efficiently.
Chris@42 174 </p>
Chris@42 175 <p>For more information regarding FFTW, see the paper, &ldquo;The Design and
Chris@42 176 Implementation of FFTW3,&rdquo; by M. Frigo and S. G. Johnson, which was an
Chris@42 177 invited paper in <cite>Proc. IEEE</cite> <b>93</b> (2), p. 216 (2005). The
Chris@42 178 code generator is described in the paper &ldquo;A fast Fourier transform
Chris@42 179 compiler&rdquo;,
Chris@42 180 <a name="index-compiler"></a>
Chris@42 181 by M. Frigo, in the <cite>Proceedings of the 1999 ACM SIGPLAN Conference
Chris@42 182 on Programming Language Design and Implementation (PLDI), Atlanta,
Chris@42 183 Georgia, May 1999</cite>. These papers, along with the latest version of
Chris@42 184 FFTW, the FAQ, benchmarks, and other links, are available at
Chris@42 185 <a href="http://www.fftw.org">the FFTW home page</a>.
Chris@42 186 </p>
Chris@42 187 <p>The current version of FFTW incorporates many good ideas from the past
Chris@42 188 thirty years of FFT literature. In one way or another, FFTW uses the
Chris@42 189 Cooley-Tukey algorithm, the prime factor algorithm, Rader&rsquo;s algorithm
Chris@42 190 for prime sizes, and a split-radix algorithm (with a
Chris@42 191 &ldquo;conjugate-pair&rdquo; variation pointed out to us by Dan Bernstein).
Chris@42 192 FFTW&rsquo;s code generator also produces new algorithms that we do not
Chris@42 193 completely understand.
Chris@42 194 <a name="index-algorithm"></a>
Chris@42 195 The reader is referred to the cited papers for the appropriate
Chris@42 196 references.
Chris@42 197 </p>
Chris@42 198 <p>The rest of this manual is organized as follows. We first discuss the
Chris@42 199 sequential (single-processor) implementation. We start by describing
Chris@42 200 the basic interface/features of FFTW in <a href="Tutorial.html#Tutorial">Tutorial</a>.
Chris@42 201 Next, <a href="Other-Important-Topics.html#Other-Important-Topics">Other Important Topics</a> discusses data alignment
Chris@42 202 (see <a href="SIMD-alignment-and-fftw_005fmalloc.html#SIMD-alignment-and-fftw_005fmalloc">SIMD alignment and fftw_malloc</a>),
Chris@42 203 the storage scheme of multi-dimensional arrays
Chris@42 204 (see <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>), and FFTW&rsquo;s mechanism for
Chris@42 205 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,
Chris@42 206 <a href="FFTW-Reference.html#FFTW-Reference">FFTW Reference</a> provides comprehensive documentation of all
Chris@42 207 FFTW&rsquo;s features. Parallel transforms are discussed in their own
Chris@42 208 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
Chris@42 209 <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
Chris@42 210 install FFTW in your computer system and how to adapt FFTW to your
Chris@42 211 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
Chris@42 212 <a href="Acknowledgments.html#Acknowledgments">Acknowledgments</a>.
Chris@42 213 </p>
Chris@42 214 <hr>
Chris@42 215 <div class="header">
Chris@42 216 <p>
Chris@42 217 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>
Chris@42 218 </div>
Chris@42 219
Chris@42 220
Chris@42 221
Chris@42 222 </body>
Chris@42 223 </html>