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Add FFTW3
author Chris Cannam <cannam@all-day-breakfast.com>
date Wed, 20 Mar 2013 15:35:50 +0000
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3 <title>Complex numbers - FFTW 3.3.3</title>
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49 <a name="Complex-numbers"></a>
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56
57 <h4 class="subsection">4.1.1 Complex numbers</h4>
58
59 <p>The default FFTW interface uses <code>double</code> precision for all
60 floating-point numbers, and defines a <code>fftw_complex</code> type to hold
61 complex numbers as:
62
63 <pre class="example"> typedef double fftw_complex[2];
64 </pre>
65 <p><a name="index-fftw_005fcomplex-139"></a>
66 Here, the <code>[0]</code> element holds the real part and the <code>[1]</code>
67 element holds the imaginary part.
68
69 <p>Alternatively, if you have a C compiler (such as <code>gcc</code>) that
70 supports the C99 revision of the ANSI C standard, you can use C's new
71 native complex type (which is binary-compatible with the typedef above).
72 In particular, if you <code>#include &lt;complex.h&gt;</code> <em>before</em>
73 <code>&lt;fftw3.h&gt;</code>, then <code>fftw_complex</code> is defined to be the native
74 complex type and you can manipulate it with ordinary arithmetic
75 (e.g. <code>x = y * (3+4*I)</code>, where <code>x</code> and <code>y</code> are
76 <code>fftw_complex</code> and <code>I</code> is the standard symbol for the
77 imaginary unit);
78 <a name="index-C99-140"></a>
79
80 <p>C++ has its own <code>complex&lt;T&gt;</code> template class, defined in the
81 standard <code>&lt;complex&gt;</code> header file. Reportedly, the C++ standards
82 committee has recently agreed to mandate that the storage format used
83 for this type be binary-compatible with the C99 type, i.e. an array
84 <code>T[2]</code> with consecutive real <code>[0]</code> and imaginary <code>[1]</code>
85 parts. (See report
86 <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
87 writing, the proposal stated that: &ldquo;This solution has been tested with
88 all current major implementations of the standard library and shown to
89 be working.&rdquo; To the extent that this is true, if you have a variable
90 <code>complex&lt;double&gt; *x</code>, you can pass it directly to FFTW via
91 <code>reinterpret_cast&lt;fftw_complex*&gt;(x)</code>.
92 <a name="index-C_002b_002b-141"></a><a name="index-portability-142"></a>
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