Mercurial > hg > sv-dependency-builds

annotate src/fftw-3.3.3/doc/html/Complex-numbers.html @ 10:37bf6b4a2645

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Add FFTW3
author Chris Cannam
date Wed, 20 Mar 2013 15:35:50 +0000
parents
children
rev   line source
Chris@10 1 <html lang="en">
Chris@10 2 <head>
Chris@10 3 <title>Complex numbers - FFTW 3.3.3</title>
Chris@10 4 <meta http-equiv="Content-Type" content="text/html">
Chris@10 5 <meta name="description" content="FFTW 3.3.3">
Chris@10 6 <meta name="generator" content="makeinfo 4.13">
Chris@10 7 <link title="Top" rel="start" href="index.html#Top">
Chris@10 8 <link rel="up" href="Data-Types-and-Files.html#Data-Types-and-Files" title="Data Types and Files">
Chris@10 9 <link rel="prev" href="Data-Types-and-Files.html#Data-Types-and-Files" title="Data Types and Files">
Chris@10 10 <link rel="next" href="Precision.html#Precision" title="Precision">
Chris@10 11 <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
Chris@10 12 <!--
Chris@10 13 This manual is for FFTW
Chris@10 14 (version 3.3.3, 25 November 2012).
Chris@10 15
Chris@10 16 Copyright (C) 2003 Matteo Frigo.
Chris@10 17
Chris@10 18 Copyright (C) 2003 Massachusetts Institute of Technology.
Chris@10 19
Chris@10 20 Permission is granted to make and distribute verbatim copies of
Chris@10 21 this manual provided the copyright notice and this permission
Chris@10 22 notice are preserved on all copies.
Chris@10 23
Chris@10 24 Permission is granted to copy and distribute modified versions of
Chris@10 25 this manual under the conditions for verbatim copying, provided
Chris@10 26 that the entire resulting derived work is distributed under the
Chris@10 27 terms of a permission notice identical to this one.
Chris@10 28
Chris@10 29 Permission is granted to copy and distribute translations of this
Chris@10 30 manual into another language, under the above conditions for
Chris@10 31 modified versions, except that this permission notice may be
Chris@10 32 stated in a translation approved by the Free Software Foundation.
Chris@10 33 -->
Chris@10 34 <meta http-equiv="Content-Style-Type" content="text/css">
Chris@10 35 <style type="text/css"><!--
Chris@10 36 pre.display { font-family:inherit }
Chris@10 37 pre.format { font-family:inherit }
Chris@10 38 pre.smalldisplay { font-family:inherit; font-size:smaller }
Chris@10 39 pre.smallformat { font-family:inherit; font-size:smaller }
Chris@10 40 pre.smallexample { font-size:smaller }
Chris@10 41 pre.smalllisp { font-size:smaller }
Chris@10 42 span.sc { font-variant:small-caps }
Chris@10 43 span.roman { font-family:serif; font-weight:normal; }
Chris@10 44 span.sansserif { font-family:sans-serif; font-weight:normal; }
Chris@10 45 --></style>
Chris@10 46 </head>
Chris@10 47 <body>
Chris@10 48 <div class="node">
Chris@10 49 <a name="Complex-numbers"></a>
Chris@10 50 <p>
Chris@10 51 Next:&nbsp;<a rel="next" accesskey="n" href="Precision.html#Precision">Precision</a>,
Chris@10 52 Previous:&nbsp;<a rel="previous" accesskey="p" href="Data-Types-and-Files.html#Data-Types-and-Files">Data Types and Files</a>,
Chris@10 53 Up:&nbsp;<a rel="up" accesskey="u" href="Data-Types-and-Files.html#Data-Types-and-Files">Data Types and Files</a>
Chris@10 54 <hr>
Chris@10 55 </div>
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 <!-- =========> -->
Chris@10 94
Chris@10 95 </body></html>
Chris@10 96