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Replace these with versions built using an older toolset (so as to avoid ABI compatibilities when linking on Ubuntu 14.04 for packaging purposes)
author Chris Cannam
date Fri, 07 Feb 2020 11:51:13 +0000
parents d0c2a83c1364
children
rev   line source
Chris@82 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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Chris@82 3 <!-- This manual is for FFTW
Chris@82 4 (version 3.3.8, 24 May 2018).
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Chris@82 6 Copyright (C) 2003 Matteo Frigo.
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Chris@82 8 Copyright (C) 2003 Massachusetts Institute of Technology.
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Chris@82 24 <head>
Chris@82 25 <title>FFTW 3.3.8: Complex numbers</title>
Chris@82 26
Chris@82 27 <meta name="description" content="FFTW 3.3.8: Complex numbers">
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Chris@82 35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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Chris@82 68 </head>
Chris@82 69
Chris@82 70 <body lang="en">
Chris@82 71 <a name="Complex-numbers"></a>
Chris@82 72 <div class="header">
Chris@82 73 <p>
Chris@82 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>
Chris@82 75 </div>
Chris@82 76 <hr>
Chris@82 77 <a name="Complex-numbers-1"></a>
Chris@82 78 <h4 class="subsection">4.1.1 Complex numbers</h4>
Chris@82 79
Chris@82 80 <p>The default FFTW interface uses <code>double</code> precision for all
Chris@82 81 floating-point numbers, and defines a <code>fftw_complex</code> type to hold
Chris@82 82 complex numbers as:
Chris@82 83 </p>
Chris@82 84 <div class="example">
Chris@82 85 <pre class="example">typedef double fftw_complex[2];
Chris@82 86 </pre></div>
Chris@82 87 <a name="index-fftw_005fcomplex-1"></a>
Chris@82 88
Chris@82 89 <p>Here, the <code>[0]</code> element holds the real part and the <code>[1]</code>
Chris@82 90 element holds the imaginary part.
Chris@82 91 </p>
Chris@82 92 <p>Alternatively, if you have a C compiler (such as <code>gcc</code>) that
Chris@82 93 supports the C99 revision of the ANSI C standard, you can use C&rsquo;s new
Chris@82 94 native complex type (which is binary-compatible with the typedef above).
Chris@82 95 In particular, if you <code>#include &lt;complex.h&gt;</code> <em>before</em>
Chris@82 96 <code>&lt;fftw3.h&gt;</code>, then <code>fftw_complex</code> is defined to be the native
Chris@82 97 complex type and you can manipulate it with ordinary arithmetic
Chris@82 98 (e.g. <code>x = y * (3+4*I)</code>, where <code>x</code> and <code>y</code> are
Chris@82 99 <code>fftw_complex</code> and <code>I</code> is the standard symbol for the
Chris@82 100 imaginary unit);
Chris@82 101 <a name="index-C99-1"></a>
Chris@82 102 </p>
Chris@82 103
Chris@82 104 <p>C++ has its own <code>complex&lt;T&gt;</code> template class, defined in the
Chris@82 105 standard <code>&lt;complex&gt;</code> header file. Reportedly, the C++ standards
Chris@82 106 committee has recently agreed to mandate that the storage format used
Chris@82 107 for this type be binary-compatible with the C99 type, i.e. an array
Chris@82 108 <code>T[2]</code> with consecutive real <code>[0]</code> and imaginary <code>[1]</code>
Chris@82 109 parts. (See report
Chris@82 110 <a href="http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf
Chris@82 111 WG21/N1388">http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf
Chris@82 112 WG21/N1388</a>.) Although not part of the official standard as of this
Chris@82 113 writing, the proposal stated that: &ldquo;This solution has been tested with
Chris@82 114 all current major implementations of the standard library and shown to
Chris@82 115 be working.&rdquo; To the extent that this is true, if you have a variable
Chris@82 116 <code>complex&lt;double&gt; *x</code>, you can pass it directly to FFTW via
Chris@82 117 <code>reinterpret_cast&lt;fftw_complex*&gt;(x)</code>.
Chris@82 118 <a name="index-C_002b_002b-3"></a>
Chris@82 119 <a name="index-portability-2"></a>
Chris@82 120 </p>
Chris@82 121
Chris@82 122
Chris@82 123
Chris@82 124 </body>
Chris@82 125 </html>