115 lines
5.1 KiB
HTML
115 lines
5.1 KiB
HTML
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<!-- This manual is for FFTW
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(version 3.3.10, 10 December 2020).
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Copyright (C) 2003 Matteo Frigo.
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Copyright (C) 2003 Massachusetts Institute of Technology.
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<title>Complex numbers (FFTW 3.3.10)</title>
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<link href="Concept-Index.html" rel="index" title="Concept Index">
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<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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<span id="Complex-numbers"></span><div class="header">
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<p>
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Next: <a href="Precision.html" accesskey="n" rel="next">Precision</a>, Previous: <a href="Data-Types-and-Files.html" accesskey="p" rel="prev">Data Types and Files</a>, Up: <a href="Data-Types-and-Files.html" accesskey="u" rel="up">Data Types and Files</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<span id="Complex-numbers-1"></span><h4 class="subsection">4.1.1 Complex numbers</h4>
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<p>The default FFTW interface uses <code>double</code> precision for all
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floating-point numbers, and defines a <code>fftw_complex</code> type to hold
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complex numbers as:
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</p>
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<div class="example">
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<pre class="example">typedef double fftw_complex[2];
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</pre></div>
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<span id="index-fftw_005fcomplex-1"></span>
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<p>Here, the <code>[0]</code> element holds the real part and the <code>[1]</code>
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element holds the imaginary part.
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</p>
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<p>Alternatively, if you have a C compiler (such as <code>gcc</code>) that
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supports the C99 revision of the ANSI C standard, you can use C’s new
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native complex type (which is binary-compatible with the typedef above).
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In particular, if you <code>#include <complex.h></code> <em>before</em>
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<code><fftw3.h></code>, then <code>fftw_complex</code> is defined to be the native
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complex type and you can manipulate it with ordinary arithmetic
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(e.g. <code>x = y * (3+4*I)</code>, where <code>x</code> and <code>y</code> are
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<code>fftw_complex</code> and <code>I</code> is the standard symbol for the
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imaginary unit);
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<span id="index-C99-1"></span>
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</p>
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<p>C++ has its own <code>complex<T></code> template class, defined in the
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standard <code><complex></code> header file. Reportedly, the C++ standards
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committee has recently agreed to mandate that the storage format used
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for this type be binary-compatible with the C99 type, i.e. an array
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<code>T[2]</code> with consecutive real <code>[0]</code> and imaginary <code>[1]</code>
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parts. (See report
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<a href="http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf
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WG21/N1388">http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf
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WG21/N1388</a>.) Although not part of the official standard as of this
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writing, the proposal stated that: “This solution has been tested with
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all current major implementations of the standard library and shown to
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be working.” To the extent that this is true, if you have a variable
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<code>complex<double> *x</code>, you can pass it directly to FFTW via
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<code>reinterpret_cast<fftw_complex*>(x)</code>.
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<span id="index-C_002b_002b-3"></span>
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<span id="index-portability-2"></span>
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</p>
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