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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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1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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3 <!-- This manual is for FFTW
4 (version 3.3.8, 24 May 2018).
5
6 Copyright (C) 2003 Matteo Frigo.
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8 Copyright (C) 2003 Massachusetts Institute of Technology.
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24 <head>
25 <title>FFTW 3.3.8: Complex numbers</title>
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71 <a name="Complex-numbers"></a>
72 <div class="header">
73 <p>
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>
75 </div>
76 <hr>
77 <a name="Complex-numbers-1"></a>
78 <h4 class="subsection">4.1.1 Complex numbers</h4>
79
80 <p>The default FFTW interface uses <code>double</code> precision for all
81 floating-point numbers, and defines a <code>fftw_complex</code> type to hold
82 complex numbers as:
83 </p>
84 <div class="example">
85 <pre class="example">typedef double fftw_complex[2];
86 </pre></div>
87 <a name="index-fftw_005fcomplex-1"></a>
88
89 <p>Here, the <code>[0]</code> element holds the real part and the <code>[1]</code>
90 element holds the imaginary part.
91 </p>
92 <p>Alternatively, if you have a C compiler (such as <code>gcc</code>) that
93 supports the C99 revision of the ANSI C standard, you can use C&rsquo;s new
94 native complex type (which is binary-compatible with the typedef above).
95 In particular, if you <code>#include &lt;complex.h&gt;</code> <em>before</em>
96 <code>&lt;fftw3.h&gt;</code>, then <code>fftw_complex</code> is defined to be the native
97 complex type and you can manipulate it with ordinary arithmetic
98 (e.g. <code>x = y * (3+4*I)</code>, where <code>x</code> and <code>y</code> are
99 <code>fftw_complex</code> and <code>I</code> is the standard symbol for the
100 imaginary unit);
101 <a name="index-C99-1"></a>
102 </p>
103
104 <p>C++ has its own <code>complex&lt;T&gt;</code> template class, defined in the
105 standard <code>&lt;complex&gt;</code> header file. Reportedly, the C++ standards
106 committee has recently agreed to mandate that the storage format used
107 for this type be binary-compatible with the C99 type, i.e. an array
108 <code>T[2]</code> with consecutive real <code>[0]</code> and imaginary <code>[1]</code>
109 parts. (See report
110 <a href="http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf
111 WG21/N1388">http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf
112 WG21/N1388</a>.) Although not part of the official standard as of this
113 writing, the proposal stated that: &ldquo;This solution has been tested with
114 all current major implementations of the standard library and shown to
115 be working.&rdquo; To the extent that this is true, if you have a variable
116 <code>complex&lt;double&gt; *x</code>, you can pass it directly to FFTW via
117 <code>reinterpret_cast&lt;fftw_complex*&gt;(x)</code>.
118 <a name="index-C_002b_002b-3"></a>
119 <a name="index-portability-2"></a>
120 </p>
121
122
123
124 </body>
125 </html>