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<a name="Complex-numbers"></a>
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<a name="Complex-numbers-1"></a>
<h4 class="subsection">4.1.1 Complex numbers</h4>

<p>The default FFTW interface uses <code>double</code> precision for all
floating-point numbers, and defines a <code>fftw_complex</code> type to hold
complex numbers as:
</p>
<div class="example">
<pre class="example">typedef double fftw_complex[2];
</pre></div>
<a name="index-fftw_005fcomplex-1"></a>

<p>Here, the <code>[0]</code> element holds the real part and the <code>[1]</code>
element holds the imaginary part.
</p>
<p>Alternatively, if you have a C compiler (such as <code>gcc</code>) that
supports the C99 revision of the ANSI C standard, you can use C&rsquo;s new
native complex type (which is binary-compatible with the typedef above).
In particular, if you <code>#include &lt;complex.h&gt;</code> <em>before</em>
<code>&lt;fftw3.h&gt;</code>, then <code>fftw_complex</code> is defined to be the native
complex type and you can manipulate it with ordinary arithmetic
(e.g. <code>x = y * (3+4*I)</code>, where <code>x</code> and <code>y</code> are
<code>fftw_complex</code> and <code>I</code> is the standard symbol for the
imaginary unit);
<a name="index-C99-1"></a>
</p>

<p>C++ has its own <code>complex&lt;T&gt;</code> template class, defined in the
standard <code>&lt;complex&gt;</code> header file.  Reportedly, the C++ standards
committee has recently agreed to mandate that the storage format used
for this type be binary-compatible with the C99 type, i.e. an array
<code>T[2]</code> with consecutive real <code>[0]</code> and imaginary <code>[1]</code>
parts.  (See report
<a href="http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf
WG21/N1388">http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf
WG21/N1388</a>.)  Although not part of the official standard as of this
writing, the proposal stated that: &ldquo;This solution has been tested with
all current major implementations of the standard library and shown to
be working.&rdquo;  To the extent that this is true, if you have a variable
<code>complex&lt;double&gt; *x</code>, you can pass it directly to FFTW via
<code>reinterpret_cast&lt;fftw_complex*&gt;(x)</code>.
<a name="index-C_002b_002b-3"></a>
<a name="index-portability-2"></a>
</p>


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author	Chris Cannam <cannam@all-day-breakfast.com>
date	Tue, 18 Oct 2016 13:40:26 +0100
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