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cannam@127: (version 3.3.5, 30 July 2016).
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cannam@127: Copyright (C) 2003 Matteo Frigo.
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cannam@127: Copyright (C) 2003 Massachusetts Institute of Technology.
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cannam@127: <title>FFTW 3.3.5: Introduction</title>
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cannam@127: <a name="Introduction"></a>
cannam@127: <div class="header">
cannam@127: <p>
cannam@127: 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: </div>
cannam@127: <hr>
cannam@127: <a name="Introduction-1"></a>
cannam@127: <h2 class="chapter">1 Introduction</h2>
cannam@127: <p>This manual documents version 3.3.5 of FFTW, the
cannam@127: <em>Fastest Fourier Transform in the West</em>.  FFTW is a comprehensive
cannam@127: collection of fast C routines for computing the discrete Fourier
cannam@127: transform (DFT) and various special cases thereof.
cannam@127: <a name="index-discrete-Fourier-transform"></a>
cannam@127: <a name="index-DFT"></a>
cannam@127: </p><ul>
cannam@127: <li> FFTW computes the DFT of complex data, real data, even-
cannam@127:   or odd-symmetric real data (these symmetric transforms are usually
cannam@127:   known as the discrete cosine or sine transform, respectively), and the
cannam@127:   discrete Hartley transform (DHT) of real data.
cannam@127: 
cannam@127: </li><li> The input data can have arbitrary length.  
cannam@127:        FFTW employs <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>) algorithms for all lengths, including
cannam@127:        prime numbers.
cannam@127: 
cannam@127: </li><li> FFTW supports arbitrary multi-dimensional data.
cannam@127: 
cannam@127: </li><li> FFTW supports the SSE, SSE2, AVX, AVX2, AVX512, KCVI, Altivec, VSX, and
cannam@127:        NEON vector instruction sets.
cannam@127: 
cannam@127: </li><li> FFTW includes parallel (multi-threaded) transforms
cannam@127:        for shared-memory systems.
cannam@127: </li><li> Starting with version 3.3, FFTW includes distributed-memory parallel
cannam@127:        transforms using MPI.
cannam@127: </li></ul>
cannam@127: 
cannam@127: <p>We assume herein that you are familiar with the properties and uses of
cannam@127: the DFT that are relevant to your application.  Otherwise, see
cannam@127: e.g. <cite>The Fast Fourier Transform and Its Applications</cite> by E. O. Brigham
cannam@127: (Prentice-Hall, Englewood Cliffs, NJ, 1988).
cannam@127: <a href="http://www.fftw.org">Our web page</a> also has links to FFT-related
cannam@127: information online.
cannam@127: <a name="index-FFTW"></a>
cannam@127: </p>
cannam@127: 
cannam@127: <p>In order to use FFTW effectively, you need to learn one basic concept
cannam@127: of FFTW&rsquo;s internal structure: FFTW does not use a fixed algorithm for
cannam@127: computing the transform, but instead it adapts the DFT algorithm to
cannam@127: details of the underlying hardware in order to maximize performance.
cannam@127: Hence, the computation of the transform is split into two phases.
cannam@127: First, FFTW&rsquo;s <em>planner</em> &ldquo;learns&rdquo; the fastest way to compute the
cannam@127: transform on your machine.  The planner
cannam@127: <a name="index-planner"></a>
cannam@127: produces a data structure called a <em>plan</em> that contains this
cannam@127: <a name="index-plan"></a>
cannam@127: information.  Subsequently, the plan is <em>executed</em>
cannam@127: <a name="index-execute"></a>
cannam@127: to transform the array of input data as dictated by the plan.  The
cannam@127: plan can be reused as many times as needed.  In typical
cannam@127: high-performance applications, many transforms of the same size are
cannam@127: computed and, consequently, a relatively expensive initialization of
cannam@127: this sort is acceptable.  On the other hand, if you need a single
cannam@127: transform of a given size, the one-time cost of the planner becomes
cannam@127: significant.  For this case, FFTW provides fast planners based on
cannam@127: heuristics or on previously computed plans.
cannam@127: </p>
cannam@127: <p>FFTW supports transforms of data with arbitrary length, rank,
cannam@127: multiplicity, and a general memory layout.  In simple cases, however,
cannam@127: this generality may be unnecessary and confusing.  Consequently, we
cannam@127: organized the interface to FFTW into three levels of increasing
cannam@127: generality.
cannam@127: </p><ul>
cannam@127: <li> The <em>basic interface</em> computes a single 
cannam@127:       transform of contiguous data.
cannam@127: </li><li> The <em>advanced interface</em> computes transforms 
cannam@127:       of multiple or strided arrays.
cannam@127: </li><li> The <em>guru interface</em> supports the most general data 
cannam@127:       layouts, multiplicities, and strides.
cannam@127: </li></ul>
cannam@127: <p>We expect that most users will be best served by the basic interface,
cannam@127: whereas the guru interface requires careful attention to the
cannam@127: documentation to avoid problems.
cannam@127: <a name="index-basic-interface"></a>
cannam@127: <a name="index-advanced-interface"></a>
cannam@127: <a name="index-guru-interface"></a>
cannam@127: </p>
cannam@127: 
cannam@127: <p>Besides the automatic performance adaptation performed by the planner,
cannam@127: it is also possible for advanced users to customize FFTW manually.  For
cannam@127: example, if code space is a concern, we provide a tool that links only
cannam@127: the subset of FFTW needed by your application.  Conversely, you may need
cannam@127: to extend FFTW because the standard distribution is not sufficient for
cannam@127: your needs.  For example, the standard FFTW distribution works most
cannam@127: efficiently for arrays whose size can be factored into small primes
cannam@127: (<em>2</em>, <em>3</em>, <em>5</em>, and <em>7</em>), and otherwise it uses a
cannam@127: slower general-purpose routine.  If you need efficient transforms of
cannam@127: other sizes, you can use FFTW&rsquo;s code generator, which produces fast C
cannam@127: programs (&ldquo;codelets&rdquo;) for any particular array size you may care
cannam@127: about.
cannam@127: <a name="index-code-generator"></a>
cannam@127: <a name="index-codelet"></a>
cannam@127: For example, if you need transforms of size
cannam@127: 513&nbsp;=&nbsp;19*3<sup>3</sup>,you can customize FFTW to support the factor <em>19</em> efficiently.
cannam@127: </p>
cannam@127: <p>For more information regarding FFTW, see the paper, &ldquo;The Design and
cannam@127: Implementation of FFTW3,&rdquo; by M. Frigo and S. G. Johnson, which was an
cannam@127: invited paper in <cite>Proc. IEEE</cite> <b>93</b> (2), p. 216 (2005).  The
cannam@127: code generator is described in the paper &ldquo;A fast Fourier transform
cannam@127: compiler&rdquo;,
cannam@127: <a name="index-compiler"></a>
cannam@127: by M. Frigo, in the <cite>Proceedings of the 1999 ACM SIGPLAN Conference
cannam@127: on Programming Language Design and Implementation (PLDI), Atlanta,
cannam@127: Georgia, May 1999</cite>.  These papers, along with the latest version of
cannam@127: FFTW, the FAQ, benchmarks, and other links, are available at
cannam@127: <a href="http://www.fftw.org">the FFTW home page</a>.  
cannam@127: </p>
cannam@127: <p>The current version of FFTW incorporates many good ideas from the past
cannam@127: thirty years of FFT literature.  In one way or another, FFTW uses the
cannam@127: Cooley-Tukey algorithm, the prime factor algorithm, Rader&rsquo;s algorithm
cannam@127: for prime sizes, and a split-radix algorithm (with a
cannam@127: &ldquo;conjugate-pair&rdquo; variation pointed out to us by Dan Bernstein).
cannam@127: FFTW&rsquo;s code generator also produces new algorithms that we do not
cannam@127: completely understand.
cannam@127: <a name="index-algorithm"></a>
cannam@127: The reader is referred to the cited papers for the appropriate
cannam@127: references.
cannam@127: </p>
cannam@127: <p>The rest of this manual is organized as follows.  We first discuss the
cannam@127: sequential (single-processor) implementation.  We start by describing
cannam@127: the basic interface/features of FFTW in <a href="Tutorial.html#Tutorial">Tutorial</a>.  
cannam@127: Next, <a href="Other-Important-Topics.html#Other-Important-Topics">Other Important Topics</a> discusses data alignment
cannam@127: (see <a href="SIMD-alignment-and-fftw_005fmalloc.html#SIMD-alignment-and-fftw_005fmalloc">SIMD alignment and fftw_malloc</a>),
cannam@127: the storage scheme of multi-dimensional arrays
cannam@127: (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: 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: <a href="FFTW-Reference.html#FFTW-Reference">FFTW Reference</a> provides comprehensive documentation of all
cannam@127: FFTW&rsquo;s features.  Parallel transforms are discussed in their own
cannam@127: 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: <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: install FFTW in your computer system and how to adapt FFTW to your
cannam@127: 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: <a href="Acknowledgments.html#Acknowledgments">Acknowledgments</a>.
cannam@127: </p>
cannam@127: <hr>
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cannam@127: <p>
cannam@127: 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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