Mercurial > hg > sv-dependency-builds

annotate src/fftw-3.3.5/doc/html/Complex-numbers.html @ 169:223a55898ab9 tip default

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Add null config files
author Chris Cannam <cannam@all-day-breakfast.com>
date Mon, 02 Mar 2020 14:03:47 +0000
parents 7867fa7e1b6b
children
rev   line source
cannam@127 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
cannam@127 2 <html>
cannam@127 3 <!-- This manual is for FFTW
cannam@127 4 (version 3.3.5, 30 July 2016).
cannam@127 5
cannam@127 6 Copyright (C) 2003 Matteo Frigo.
cannam@127 7
cannam@127 8 Copyright (C) 2003 Massachusetts Institute of Technology.
cannam@127 9
cannam@127 10 Permission is granted to make and distribute verbatim copies of this
cannam@127 11 manual provided the copyright notice and this permission notice are
cannam@127 12 preserved on all copies.
cannam@127 13
cannam@127 14 Permission is granted to copy and distribute modified versions of this
cannam@127 15 manual under the conditions for verbatim copying, provided that the
cannam@127 16 entire resulting derived work is distributed under the terms of a
cannam@127 17 permission notice identical to this one.
cannam@127 18
cannam@127 19 Permission is granted to copy and distribute translations of this manual
cannam@127 20 into another language, under the above conditions for modified versions,
cannam@127 21 except that this permission notice may be stated in a translation
cannam@127 22 approved by the Free Software Foundation. -->
cannam@127 23 <!-- Created by GNU Texinfo 5.2, http://www.gnu.org/software/texinfo/ -->
cannam@127 24 <head>
cannam@127 25 <title>FFTW 3.3.5: Complex numbers</title>
cannam@127 26
cannam@127 27 <meta name="description" content="FFTW 3.3.5: Complex numbers">
cannam@127 28 <meta name="keywords" content="FFTW 3.3.5: Complex numbers">
cannam@127 29 <meta name="resource-type" content="document">
cannam@127 30 <meta name="distribution" content="global">
cannam@127 31 <meta name="Generator" content="makeinfo">
cannam@127 32 <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
cannam@127 33 <link href="index.html#Top" rel="start" title="Top">
cannam@127 34 <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
cannam@127 35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
cannam@127 36 <link href="Data-Types-and-Files.html#Data-Types-and-Files" rel="up" title="Data Types and Files">
cannam@127 37 <link href="Precision.html#Precision" rel="next" title="Precision">
cannam@127 38 <link href="Data-Types-and-Files.html#Data-Types-and-Files" rel="prev" title="Data Types and Files">
cannam@127 39 <style type="text/css">
cannam@127 40 <!--
cannam@127 41 a.summary-letter {text-decoration: none}
cannam@127 42 blockquote.smallquotation {font-size: smaller}
cannam@127 43 div.display {margin-left: 3.2em}
cannam@127 44 div.example {margin-left: 3.2em}
cannam@127 45 div.indentedblock {margin-left: 3.2em}
cannam@127 46 div.lisp {margin-left: 3.2em}
cannam@127 47 div.smalldisplay {margin-left: 3.2em}
cannam@127 48 div.smallexample {margin-left: 3.2em}
cannam@127 49 div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
cannam@127 50 div.smalllisp {margin-left: 3.2em}
cannam@127 51 kbd {font-style:oblique}
cannam@127 52 pre.display {font-family: inherit}
cannam@127 53 pre.format {font-family: inherit}
cannam@127 54 pre.menu-comment {font-family: serif}
cannam@127 55 pre.menu-preformatted {font-family: serif}
cannam@127 56 pre.smalldisplay {font-family: inherit; font-size: smaller}
cannam@127 57 pre.smallexample {font-size: smaller}
cannam@127 58 pre.smallformat {font-family: inherit; font-size: smaller}
cannam@127 59 pre.smalllisp {font-size: smaller}
cannam@127 60 span.nocodebreak {white-space:nowrap}
cannam@127 61 span.nolinebreak {white-space:nowrap}
cannam@127 62 span.roman {font-family:serif; font-weight:normal}
cannam@127 63 span.sansserif {font-family:sans-serif; font-weight:normal}
cannam@127 64 ul.no-bullet {list-style: none}
cannam@127 65 -->
cannam@127 66 </style>
cannam@127 67
cannam@127 68
cannam@127 69 </head>
cannam@127 70
cannam@127 71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
cannam@127 72 <a name="Complex-numbers"></a>
cannam@127 73 <div class="header">
cannam@127 74 <p>
cannam@127 75 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>
cannam@127 76 </div>
cannam@127 77 <hr>
cannam@127 78 <a name="Complex-numbers-1"></a>
cannam@127 79 <h4 class="subsection">4.1.1 Complex numbers</h4>
cannam@127 80
cannam@127 81 <p>The default FFTW interface uses <code>double</code> precision for all
cannam@127 82 floating-point numbers, and defines a <code>fftw_complex</code> type to hold
cannam@127 83 complex numbers as:
cannam@127 84 </p>
cannam@127 85 <div class="example">
cannam@127 86 <pre class="example">typedef double fftw_complex[2];
cannam@127 87 </pre></div>
cannam@127 88 <a name="index-fftw_005fcomplex-1"></a>
cannam@127 89
cannam@127 90 <p>Here, the <code>[0]</code> element holds the real part and the <code>[1]</code>
cannam@127 91 element holds the imaginary part.
cannam@127 92 </p>
cannam@127 93 <p>Alternatively, if you have a C compiler (such as <code>gcc</code>) that
cannam@127 94 supports the C99 revision of the ANSI C standard, you can use C&rsquo;s new
cannam@127 95 native complex type (which is binary-compatible with the typedef above).
cannam@127 96 In particular, if you <code>#include &lt;complex.h&gt;</code> <em>before</em>
cannam@127 97 <code>&lt;fftw3.h&gt;</code>, then <code>fftw_complex</code> is defined to be the native
cannam@127 98 complex type and you can manipulate it with ordinary arithmetic
cannam@127 99 (e.g. <code>x = y * (3+4*I)</code>, where <code>x</code> and <code>y</code> are
cannam@127 100 <code>fftw_complex</code> and <code>I</code> is the standard symbol for the
cannam@127 101 imaginary unit);
cannam@127 102 <a name="index-C99-1"></a>
cannam@127 103 </p>
cannam@127 104
cannam@127 105 <p>C++ has its own <code>complex&lt;T&gt;</code> template class, defined in the
cannam@127 106 standard <code>&lt;complex&gt;</code> header file. Reportedly, the C++ standards
cannam@127 107 committee has recently agreed to mandate that the storage format used
cannam@127 108 for this type be binary-compatible with the C99 type, i.e. an array
cannam@127 109 <code>T[2]</code> with consecutive real <code>[0]</code> and imaginary <code>[1]</code>
cannam@127 110 parts. (See report
cannam@127 111 <a href="http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf
cannam@127 112 WG21/N1388">http://www.open-std.org/jtc1/sc22/WG21/docs/papers/2002/n1388.pdf
cannam@127 113 WG21/N1388</a>.) Although not part of the official standard as of this
cannam@127 114 writing, the proposal stated that: &ldquo;This solution has been tested with
cannam@127 115 all current major implementations of the standard library and shown to
cannam@127 116 be working.&rdquo; To the extent that this is true, if you have a variable
cannam@127 117 <code>complex&lt;double&gt; *x</code>, you can pass it directly to FFTW via
cannam@127 118 <code>reinterpret_cast&lt;fftw_complex*&gt;(x)</code>.
cannam@127 119 <a name="index-C_002b_002b-3"></a>
cannam@127 120 <a name="index-portability-2"></a>
cannam@127 121 </p>
cannam@127 122
cannam@127 123
cannam@127 124
cannam@127 125 </body>
cannam@127 126 </html>