Mercurial > hg > sv-dependency-builds

annotate src/fftw-3.3.8/doc/html/Complex-numbers.html @ 82:d0c2a83c1364

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Add FFTW 3.3.8 source, and a Linux build
author Chris Cannam
date Tue, 19 Nov 2019 14:52:55 +0000
parents
children
rev   line source
Chris@82 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
Chris@82 2 <html>
Chris@82 3 <!-- This manual is for FFTW
Chris@82 4 (version 3.3.8, 24 May 2018).
Chris@82 5
Chris@82 6 Copyright (C) 2003 Matteo Frigo.
Chris@82 7
Chris@82 8 Copyright (C) 2003 Massachusetts Institute of Technology.
Chris@82 9
Chris@82 10 Permission is granted to make and distribute verbatim copies of this
Chris@82 11 manual provided the copyright notice and this permission notice are
Chris@82 12 preserved on all copies.
Chris@82 13
Chris@82 14 Permission is granted to copy and distribute modified versions of this
Chris@82 15 manual under the conditions for verbatim copying, provided that the
Chris@82 16 entire resulting derived work is distributed under the terms of a
Chris@82 17 permission notice identical to this one.
Chris@82 18
Chris@82 19 Permission is granted to copy and distribute translations of this manual
Chris@82 20 into another language, under the above conditions for modified versions,
Chris@82 21 except that this permission notice may be stated in a translation
Chris@82 22 approved by the Free Software Foundation. -->
Chris@82 23 <!-- Created by GNU Texinfo 6.3, http://www.gnu.org/software/texinfo/ -->
Chris@82 24 <head>
Chris@82 25 <title>FFTW 3.3.8: Complex numbers</title>
Chris@82 26
Chris@82 27 <meta name="description" content="FFTW 3.3.8: Complex numbers">
Chris@82 28 <meta name="keywords" content="FFTW 3.3.8: Complex numbers">
Chris@82 29 <meta name="resource-type" content="document">
Chris@82 30 <meta name="distribution" content="global">
Chris@82 31 <meta name="Generator" content="makeinfo">
Chris@82 32 <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
Chris@82 33 <link href="index.html#Top" rel="start" title="Top">
Chris@82 34 <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
Chris@82 35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
Chris@82 36 <link href="Data-Types-and-Files.html#Data-Types-and-Files" rel="up" title="Data Types and Files">
Chris@82 37 <link href="Precision.html#Precision" rel="next" title="Precision">
Chris@82 38 <link href="Data-Types-and-Files.html#Data-Types-and-Files" rel="prev" title="Data Types and Files">
Chris@82 39 <style type="text/css">
Chris@82 40 <!--
Chris@82 41 a.summary-letter {text-decoration: none}
Chris@82 42 blockquote.indentedblock {margin-right: 0em}
Chris@82 43 blockquote.smallindentedblock {margin-right: 0em; font-size: smaller}
Chris@82 44 blockquote.smallquotation {font-size: smaller}
Chris@82 45 div.display {margin-left: 3.2em}
Chris@82 46 div.example {margin-left: 3.2em}
Chris@82 47 div.lisp {margin-left: 3.2em}
Chris@82 48 div.smalldisplay {margin-left: 3.2em}
Chris@82 49 div.smallexample {margin-left: 3.2em}
Chris@82 50 div.smalllisp {margin-left: 3.2em}
Chris@82 51 kbd {font-style: oblique}
Chris@82 52 pre.display {font-family: inherit}
Chris@82 53 pre.format {font-family: inherit}
Chris@82 54 pre.menu-comment {font-family: serif}
Chris@82 55 pre.menu-preformatted {font-family: serif}
Chris@82 56 pre.smalldisplay {font-family: inherit; font-size: smaller}
Chris@82 57 pre.smallexample {font-size: smaller}
Chris@82 58 pre.smallformat {font-family: inherit; font-size: smaller}
Chris@82 59 pre.smalllisp {font-size: smaller}
Chris@82 60 span.nolinebreak {white-space: nowrap}
Chris@82 61 span.roman {font-family: initial; font-weight: normal}
Chris@82 62 span.sansserif {font-family: sans-serif; font-weight: normal}
Chris@82 63 ul.no-bullet {list-style: none}
Chris@82 64 -->
Chris@82 65 </style>
Chris@82 66
Chris@82 67
Chris@82 68 </head>
Chris@82 69
Chris@82 70 <body lang="en">
Chris@82 71 <a name="Complex-numbers"></a>
Chris@82 72 <div class="header">
Chris@82 73 <p>
Chris@82 74 Next: <a href="Precision.html#Precision" accesskey="n" rel="next">Precision</a>, Previous: <a href="Data-Types-and-Files.html#Data-Types-and-Files" accesskey="p" rel="prev">Data Types and Files</a>, Up: <a href="Data-Types-and-Files.html#Data-Types-and-Files" accesskey="u" rel="up">Data Types and Files</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
Chris@82 75 </div>
Chris@82 76 <hr>
Chris@82 77 <a name="Complex-numbers-1"></a>
Chris@82 78 <h4 class="subsection">4.1.1 Complex numbers</h4>
Chris@82 79
Chris@82 80 <p>The default FFTW interface uses <code>double</code> precision for all
Chris@82 81 floating-point numbers, and defines a <code>fftw_complex</code> type to hold
Chris@82 82 complex numbers as:
Chris@82 83 </p>
Chris@82 84 <div class="example">
Chris@82 85 <pre class="example">typedef double fftw_complex[2];
Chris@82 86 </pre></div>
Chris@82 87 <a name="index-fftw_005fcomplex-1"></a>
Chris@82 88
Chris@82 89 <p>Here, the <code>[0]</code> element holds the real part and the <code>[1]</code>
Chris@82 90 element holds the imaginary part.
Chris@82 91 </p>
Chris@82 92 <p>Alternatively, if you have a C compiler (such as <code>gcc</code>) that
Chris@82 93 supports the C99 revision of the ANSI C standard, you can use C&rsquo;s new
Chris@82 94 native complex type (which is binary-compatible with the typedef above).
Chris@82 95 In particular, if you <code>#include &lt;complex.h&gt;</code> <em>before</em>
Chris@82 96 <code>&lt;fftw3.h&gt;</code>, then <code>fftw_complex</code> is defined to be the native
Chris@82 97 complex type and you can manipulate it with ordinary arithmetic
Chris@82 98 (e.g. <code>x = y * (3+4*I)</code>, where <code>x</code> and <code>y</code> are
Chris@82 99 <code>fftw_complex</code> and <code>I</code> is the standard symbol for the
Chris@82 100 imaginary unit);
Chris@82 101 <a name="index-C99-1"></a>
Chris@82 102 </p>
Chris@82 103
Chris@82 104 <p>C++ has its own <code>complex&lt;T&gt;</code> template class, defined in the
Chris@82 105 standard <code>&lt;complex&gt;</code> header file. Reportedly, the C++ standards
Chris@82 106 committee has recently agreed to mandate that the storage format used
Chris@82 107 for this type be binary-compatible with the C99 type, i.e. an array
Chris@82 108 <code>T[2]</code> with consecutive real <code>[0]</code> and imaginary <code>[1]</code>
Chris@82 109 parts. (See report
Chris@82 110 <a href="http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf
Chris@82 111 WG21/N1388">http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf
Chris@82 112 WG21/N1388</a>.) Although not part of the official standard as of this
Chris@82 113 writing, the proposal stated that: &ldquo;This solution has been tested with
Chris@82 114 all current major implementations of the standard library and shown to
Chris@82 115 be working.&rdquo; To the extent that this is true, if you have a variable
Chris@82 116 <code>complex&lt;double&gt; *x</code>, you can pass it directly to FFTW via
Chris@82 117 <code>reinterpret_cast&lt;fftw_complex*&gt;(x)</code>.
Chris@82 118 <a name="index-C_002b_002b-3"></a>
Chris@82 119 <a name="index-portability-2"></a>
Chris@82 120 </p>
Chris@82 121
Chris@82 122
Chris@82 123
Chris@82 124 </body>
Chris@82 125 </html>