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3 <title>Complex numbers - FFTW 3.2.1</title>
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4 <meta http-equiv="Content-Type" content="text/html">
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5 <meta name="description" content="FFTW 3.2.1">
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12 <!--
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13 This manual is for FFTW
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14 (version 3.2.1, 5 February 2009).
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15
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16 Copyright (C) 2003 Matteo Frigo.
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17
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18 Copyright (C) 2003 Massachusetts Institute of Technology.
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19
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20 Permission is granted to make and distribute verbatim copies of
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21 this manual provided the copyright notice and this permission
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22 notice are preserved on all copies.
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23
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24 Permission is granted to copy and distribute modified versions of
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25 this manual under the conditions for verbatim copying, provided
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26 that the entire resulting derived work is distributed under the
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27 terms of a permission notice identical to this one.
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28
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29 Permission is granted to copy and distribute translations of this
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30 manual into another language, under the above conditions for
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31 modified versions, except that this permission notice may be
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32 stated in a translation approved by the Free Software Foundation.
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33 -->
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45 --></style>
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46 </head>
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47 <body>
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48 <div class="node">
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49 <p>
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50 <a name="Complex-numbers"></a>
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51 Next: <a rel="next" accesskey="n" href="Precision.html#Precision">Precision</a>,
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52 Previous: <a rel="previous" accesskey="p" href="Data-Types-and-Files.html#Data-Types-and-Files">Data Types and Files</a>,
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53 Up: <a rel="up" accesskey="u" href="Data-Types-and-Files.html#Data-Types-and-Files">Data Types and Files</a>
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54 <hr>
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55 </div>
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56
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57 <h4 class="subsection">4.1.1 Complex numbers</h4>
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58
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59 <p>The default FFTW interface uses <code>double</code> precision for all
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60 floating-point numbers, and defines a <code>fftw_complex</code> type to hold
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61 complex numbers as:
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62
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63 <pre class="example"> typedef double fftw_complex[2];
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64 </pre>
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65 <p><a name="index-fftw_005fcomplex-136"></a>
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66 Here, the <code>[0]</code> element holds the real part and the <code>[1]</code>
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67 element holds the imaginary part.
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68
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69 <p>Alternatively, if you have a C compiler (such as <code>gcc</code>) that
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70 supports the C99 revision of the ANSI C standard, you can use C's new
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71 native complex type (which is binary-compatible with the typedef above).
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72 In particular, if you <code>#include <complex.h></code> <em>before</em>
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73 <code><fftw3.h></code>, then <code>fftw_complex</code> is defined to be the native
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74 complex type and you can manipulate it with ordinary arithmetic
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75 (e.g. <code>x = y * (3+4*I)</code>, where <code>x</code> and <code>y</code> are
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76 <code>fftw_complex</code> and <code>I</code> is the standard symbol for the
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77 imaginary unit);
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78 <a name="index-C99-137"></a>
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79 C++ has its own <code>complex<T></code> template class, defined in the
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80 standard <code><complex></code> header file. Reportedly, the C++ standards
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81 committee has recently agreed to mandate that the storage format used
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82 for this type be binary-compatible with the C99 type, i.e. an array
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83 <code>T[2]</code> with consecutive real <code>[0]</code> and imaginary <code>[1]</code>
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84 parts. (See report
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85 <a href="http://anubis.dkuug.dk/JTC1/SC22/WG21/docs/papers/2002/1388.pdf">WG21/N1388</a>.) Although not part of the official standard as of this
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86 writing, the proposal stated that: “This solution has been tested with
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87 all current major implementations of the standard library and shown to
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88 be working.” To the extent that this is true, if you have a variable
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89 <code>complex<double> *x</code>, you can pass it directly to FFTW via
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90 <code>reinterpret_cast<fftw_complex*>(x)</code>.
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91 <a name="index-C_002b_002b-138"></a><a name="index-portability-139"></a>
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92 <!-- =========> -->
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93
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94 </body></html>
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95
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