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Current fftw source
author Chris Cannam
date Tue, 18 Oct 2016 13:40:26 +0100
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3 <!-- This manual is for FFTW
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25 <title>FFTW 3.3.5: Complex numbers</title>
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72 <a name="Complex-numbers"></a>
73 <div class="header">
74 <p>
75 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>
76 </div>
77 <hr>
78 <a name="Complex-numbers-1"></a>
79 <h4 class="subsection">4.1.1 Complex numbers</h4>
80
81 <p>The default FFTW interface uses <code>double</code> precision for all
82 floating-point numbers, and defines a <code>fftw_complex</code> type to hold
83 complex numbers as:
84 </p>
85 <div class="example">
86 <pre class="example">typedef double fftw_complex[2];
87 </pre></div>
88 <a name="index-fftw_005fcomplex-1"></a>
89
90 <p>Here, the <code>[0]</code> element holds the real part and the <code>[1]</code>
91 element holds the imaginary part.
92 </p>
93 <p>Alternatively, if you have a C compiler (such as <code>gcc</code>) that
94 supports the C99 revision of the ANSI C standard, you can use C&rsquo;s new
95 native complex type (which is binary-compatible with the typedef above).
96 In particular, if you <code>#include &lt;complex.h&gt;</code> <em>before</em>
97 <code>&lt;fftw3.h&gt;</code>, then <code>fftw_complex</code> is defined to be the native
98 complex type and you can manipulate it with ordinary arithmetic
99 (e.g. <code>x = y * (3+4*I)</code>, where <code>x</code> and <code>y</code> are
100 <code>fftw_complex</code> and <code>I</code> is the standard symbol for the
101 imaginary unit);
102 <a name="index-C99-1"></a>
103 </p>
104
105 <p>C++ has its own <code>complex&lt;T&gt;</code> template class, defined in the
106 standard <code>&lt;complex&gt;</code> header file. Reportedly, the C++ standards
107 committee has recently agreed to mandate that the storage format used
108 for this type be binary-compatible with the C99 type, i.e. an array
109 <code>T[2]</code> with consecutive real <code>[0]</code> and imaginary <code>[1]</code>
110 parts. (See report
111 <a href="http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf
112 WG21/N1388">http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf
113 WG21/N1388</a>.) Although not part of the official standard as of this
114 writing, the proposal stated that: &ldquo;This solution has been tested with
115 all current major implementations of the standard library and shown to
116 be working.&rdquo; To the extent that this is true, if you have a variable
117 <code>complex&lt;double&gt; *x</code>, you can pass it directly to FFTW via
118 <code>reinterpret_cast&lt;fftw_complex*&gt;(x)</code>.
119 <a name="index-C_002b_002b-3"></a>
120 <a name="index-portability-2"></a>
121 </p>
122
123
124
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