Mercurial > hg > sv-dependency-builds
diff src/fftw-3.3.8/doc/html/Complex-numbers.html @ 167:bd3cc4d1df30
Add FFTW 3.3.8 source, and a Linux build
| author | Chris Cannam <cannam@all-day-breakfast.com> |
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| date | Tue, 19 Nov 2019 14:52:55 +0000 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/fftw-3.3.8/doc/html/Complex-numbers.html Tue Nov 19 14:52:55 2019 +0000 @@ -0,0 +1,125 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> +<html> +<!-- This manual is for FFTW +(version 3.3.8, 24 May 2018). + +Copyright (C) 2003 Matteo Frigo. + +Copyright (C) 2003 Massachusetts Institute of Technology. + +Permission is granted to make and distribute verbatim copies of this +manual provided the copyright notice and this permission notice are +preserved on all copies. + +Permission is granted to copy and distribute modified versions of this +manual under the conditions for verbatim copying, provided that the +entire resulting derived work is distributed under the terms of a +permission notice identical to this one. + +Permission is granted to copy and distribute translations of this manual +into another language, under the above conditions for modified versions, +except that this permission notice may be stated in a translation +approved by the Free Software Foundation. --> +<!-- Created by GNU Texinfo 6.3, http://www.gnu.org/software/texinfo/ --> +<head> +<title>FFTW 3.3.8: Complex numbers</title> + +<meta name="description" content="FFTW 3.3.8: Complex numbers"> +<meta name="keywords" content="FFTW 3.3.8: Complex numbers"> +<meta name="resource-type" content="document"> +<meta name="distribution" content="global"> +<meta name="Generator" content="makeinfo"> +<meta http-equiv="Content-Type" content="text/html; charset=utf-8"> +<link href="index.html#Top" rel="start" title="Top"> +<link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index"> +<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents"> +<link href="Data-Types-and-Files.html#Data-Types-and-Files" rel="up" title="Data Types and Files"> +<link href="Precision.html#Precision" rel="next" title="Precision"> +<link href="Data-Types-and-Files.html#Data-Types-and-Files" rel="prev" title="Data Types and Files"> +<style type="text/css"> +<!-- +a.summary-letter {text-decoration: none} +blockquote.indentedblock {margin-right: 0em} +blockquote.smallindentedblock {margin-right: 0em; font-size: smaller} +blockquote.smallquotation {font-size: smaller} +div.display {margin-left: 3.2em} +div.example {margin-left: 3.2em} +div.lisp {margin-left: 3.2em} +div.smalldisplay {margin-left: 3.2em} +div.smallexample {margin-left: 3.2em} +div.smalllisp {margin-left: 3.2em} +kbd {font-style: oblique} +pre.display {font-family: inherit} +pre.format {font-family: inherit} +pre.menu-comment {font-family: serif} +pre.menu-preformatted {font-family: serif} +pre.smalldisplay {font-family: inherit; font-size: smaller} +pre.smallexample {font-size: smaller} +pre.smallformat {font-family: inherit; font-size: smaller} +pre.smalllisp {font-size: smaller} +span.nolinebreak {white-space: nowrap} +span.roman {font-family: initial; font-weight: normal} +span.sansserif {font-family: sans-serif; font-weight: normal} +ul.no-bullet {list-style: none} +--> +</style> + + +</head> + +<body lang="en"> +<a name="Complex-numbers"></a> +<div class="header"> +<p> +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> [<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> +</div> +<hr> +<a name="Complex-numbers-1"></a> +<h4 class="subsection">4.1.1 Complex numbers</h4> + +<p>The default FFTW interface uses <code>double</code> precision for all +floating-point numbers, and defines a <code>fftw_complex</code> type to hold +complex numbers as: +</p> +<div class="example"> +<pre class="example">typedef double fftw_complex[2]; +</pre></div> +<a name="index-fftw_005fcomplex-1"></a> + +<p>Here, the <code>[0]</code> element holds the real part and the <code>[1]</code> +element holds the imaginary part. +</p> +<p>Alternatively, if you have a C compiler (such as <code>gcc</code>) that +supports the C99 revision of the ANSI C standard, you can use C’s new +native complex type (which is binary-compatible with the typedef above). +In particular, if you <code>#include <complex.h></code> <em>before</em> +<code><fftw3.h></code>, then <code>fftw_complex</code> is defined to be the native +complex type and you can manipulate it with ordinary arithmetic +(e.g. <code>x = y * (3+4*I)</code>, where <code>x</code> and <code>y</code> are +<code>fftw_complex</code> and <code>I</code> is the standard symbol for the +imaginary unit); +<a name="index-C99-1"></a> +</p> + +<p>C++ has its own <code>complex<T></code> template class, defined in the +standard <code><complex></code> header file. Reportedly, the C++ standards +committee has recently agreed to mandate that the storage format used +for this type be binary-compatible with the C99 type, i.e. an array +<code>T[2]</code> with consecutive real <code>[0]</code> and imaginary <code>[1]</code> +parts. (See report +<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 +writing, the proposal stated that: “This solution has been tested with +all current major implementations of the standard library and shown to +be working.” To the extent that this is true, if you have a variable +<code>complex<double> *x</code>, you can pass it directly to FFTW via +<code>reinterpret_cast<fftw_complex*>(x)</code>. +<a name="index-C_002b_002b-3"></a> +<a name="index-portability-2"></a> +</p> + + + +</body> +</html>