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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 37bf6b4a2645
children
rev   line source
Chris@10 1 <html lang="en">
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Chris@10 3 <title>Complex numbers - FFTW 3.3.3</title>
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Chris@10 49 <a name="Complex-numbers"></a>
Chris@10 50 <p>
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Chris@10 56
Chris@10 57 <h4 class="subsection">4.1.1 Complex numbers</h4>
Chris@10 58
Chris@10 59 <p>The default FFTW interface uses <code>double</code> precision for all
Chris@10 60 floating-point numbers, and defines a <code>fftw_complex</code> type to hold
Chris@10 61 complex numbers as:
Chris@10 62
Chris@10 63 <pre class="example"> typedef double fftw_complex[2];
Chris@10 64 </pre>
Chris@10 65 <p><a name="index-fftw_005fcomplex-139"></a>
Chris@10 66 Here, the <code>[0]</code> element holds the real part and the <code>[1]</code>
Chris@10 67 element holds the imaginary part.
Chris@10 68
Chris@10 69 <p>Alternatively, if you have a C compiler (such as <code>gcc</code>) that
Chris@10 70 supports the C99 revision of the ANSI C standard, you can use C's new
Chris@10 71 native complex type (which is binary-compatible with the typedef above).
Chris@10 72 In particular, if you <code>#include &lt;complex.h&gt;</code> <em>before</em>
Chris@10 73 <code>&lt;fftw3.h&gt;</code>, then <code>fftw_complex</code> is defined to be the native
Chris@10 74 complex type and you can manipulate it with ordinary arithmetic
Chris@10 75 (e.g. <code>x = y * (3+4*I)</code>, where <code>x</code> and <code>y</code> are
Chris@10 76 <code>fftw_complex</code> and <code>I</code> is the standard symbol for the
Chris@10 77 imaginary unit);
Chris@10 78 <a name="index-C99-140"></a>
Chris@10 79
Chris@10 80 <p>C++ has its own <code>complex&lt;T&gt;</code> template class, defined in the
Chris@10 81 standard <code>&lt;complex&gt;</code> header file. Reportedly, the C++ standards
Chris@10 82 committee has recently agreed to mandate that the storage format used
Chris@10 83 for this type be binary-compatible with the C99 type, i.e. an array
Chris@10 84 <code>T[2]</code> with consecutive real <code>[0]</code> and imaginary <code>[1]</code>
Chris@10 85 parts. (See report
Chris@10 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
Chris@10 87 writing, the proposal stated that: &ldquo;This solution has been tested with
Chris@10 88 all current major implementations of the standard library and shown to
Chris@10 89 be working.&rdquo; To the extent that this is true, if you have a variable
Chris@10 90 <code>complex&lt;double&gt; *x</code>, you can pass it directly to FFTW via
Chris@10 91 <code>reinterpret_cast&lt;fftw_complex*&gt;(x)</code>.
Chris@10 92 <a name="index-C_002b_002b-141"></a><a name="index-portability-142"></a>
Chris@10 93 <!-- =========> -->
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