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Add FFTW 3.3.8 source, and a Linux build
author Chris Cannam <cannam@all-day-breakfast.com>
date Tue, 19 Nov 2019 14:52:55 +0000
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cannam@167 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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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: Complex numbers</title>
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cannam@167 70 <body lang="en">
cannam@167 71 <a name="Complex-numbers"></a>
cannam@167 72 <div class="header">
cannam@167 73 <p>
cannam@167 74 Next: <a href="Precision.html#Precision" accesskey="n" rel="next">Precision</a>, Previous: <a href="Data-Types-and-Files.html#Data-Types-and-Files" accesskey="p" rel="prev">Data Types and Files</a>, Up: <a href="Data-Types-and-Files.html#Data-Types-and-Files" accesskey="u" rel="up">Data Types and Files</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="Complex-numbers-1"></a>
cannam@167 78 <h4 class="subsection">4.1.1 Complex numbers</h4>
cannam@167 79
cannam@167 80 <p>The default FFTW interface uses <code>double</code> precision for all
cannam@167 81 floating-point numbers, and defines a <code>fftw_complex</code> type to hold
cannam@167 82 complex numbers as:
cannam@167 83 </p>
cannam@167 84 <div class="example">
cannam@167 85 <pre class="example">typedef double fftw_complex[2];
cannam@167 86 </pre></div>
cannam@167 87 <a name="index-fftw_005fcomplex-1"></a>
cannam@167 88
cannam@167 89 <p>Here, the <code>[0]</code> element holds the real part and the <code>[1]</code>
cannam@167 90 element holds the imaginary part.
cannam@167 91 </p>
cannam@167 92 <p>Alternatively, if you have a C compiler (such as <code>gcc</code>) that
cannam@167 93 supports the C99 revision of the ANSI C standard, you can use C&rsquo;s new
cannam@167 94 native complex type (which is binary-compatible with the typedef above).
cannam@167 95 In particular, if you <code>#include &lt;complex.h&gt;</code> <em>before</em>
cannam@167 96 <code>&lt;fftw3.h&gt;</code>, then <code>fftw_complex</code> is defined to be the native
cannam@167 97 complex type and you can manipulate it with ordinary arithmetic
cannam@167 98 (e.g. <code>x = y * (3+4*I)</code>, where <code>x</code> and <code>y</code> are
cannam@167 99 <code>fftw_complex</code> and <code>I</code> is the standard symbol for the
cannam@167 100 imaginary unit);
cannam@167 101 <a name="index-C99-1"></a>
cannam@167 102 </p>
cannam@167 103
cannam@167 104 <p>C++ has its own <code>complex&lt;T&gt;</code> template class, defined in the
cannam@167 105 standard <code>&lt;complex&gt;</code> header file. Reportedly, the C++ standards
cannam@167 106 committee has recently agreed to mandate that the storage format used
cannam@167 107 for this type be binary-compatible with the C99 type, i.e. an array
cannam@167 108 <code>T[2]</code> with consecutive real <code>[0]</code> and imaginary <code>[1]</code>
cannam@167 109 parts. (See report
cannam@167 110 <a href="http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf
cannam@167 111 WG21/N1388">http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf
cannam@167 112 WG21/N1388</a>.) Although not part of the official standard as of this
cannam@167 113 writing, the proposal stated that: &ldquo;This solution has been tested with
cannam@167 114 all current major implementations of the standard library and shown to
cannam@167 115 be working.&rdquo; To the extent that this is true, if you have a variable
cannam@167 116 <code>complex&lt;double&gt; *x</code>, you can pass it directly to FFTW via
cannam@167 117 <code>reinterpret_cast&lt;fftw_complex*&gt;(x)</code>.
cannam@167 118 <a name="index-C_002b_002b-3"></a>
cannam@167 119 <a name="index-portability-2"></a>
cannam@167 120 </p>
cannam@167 121
cannam@167 122
cannam@167 123
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