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diff src/fftw-3.3.3/doc/html/Complex-numbers.html @ 95:89f5e221ed7b
Add FFTW3
| author | Chris Cannam <cannam@all-day-breakfast.com> |
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| date | Wed, 20 Mar 2013 15:35:50 +0000 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/fftw-3.3.3/doc/html/Complex-numbers.html Wed Mar 20 15:35:50 2013 +0000 @@ -0,0 +1,96 @@ +<html lang="en"> +<head> +<title>Complex numbers - FFTW 3.3.3</title> +<meta http-equiv="Content-Type" content="text/html"> +<meta name="description" content="FFTW 3.3.3"> +<meta name="generator" content="makeinfo 4.13"> +<link title="Top" rel="start" href="index.html#Top"> +<link rel="up" href="Data-Types-and-Files.html#Data-Types-and-Files" title="Data Types and Files"> +<link rel="prev" href="Data-Types-and-Files.html#Data-Types-and-Files" title="Data Types and Files"> +<link rel="next" href="Precision.html#Precision" title="Precision"> +<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage"> +<!-- +This manual is for FFTW +(version 3.3.3, 25 November 2012). + +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. + --> +<meta http-equiv="Content-Style-Type" content="text/css"> +<style type="text/css"><!-- + pre.display { font-family:inherit } + pre.format { font-family:inherit } + pre.smalldisplay { font-family:inherit; font-size:smaller } + pre.smallformat { font-family:inherit; font-size:smaller } + pre.smallexample { font-size:smaller } + pre.smalllisp { font-size:smaller } + span.sc { font-variant:small-caps } + span.roman { font-family:serif; font-weight:normal; } + span.sansserif { font-family:sans-serif; font-weight:normal; } +--></style> +</head> +<body> +<div class="node"> +<a name="Complex-numbers"></a> +<p> +Next: <a rel="next" accesskey="n" href="Precision.html#Precision">Precision</a>, +Previous: <a rel="previous" accesskey="p" href="Data-Types-and-Files.html#Data-Types-and-Files">Data Types and Files</a>, +Up: <a rel="up" accesskey="u" href="Data-Types-and-Files.html#Data-Types-and-Files">Data Types and Files</a> +<hr> +</div> + +<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: + +<pre class="example"> typedef double fftw_complex[2]; +</pre> + <p><a name="index-fftw_005fcomplex-139"></a> +Here, the <code>[0]</code> element holds the real part and the <code>[1]</code> +element holds the imaginary part. + + <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-C99-140"></a> + + <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-141"></a><a name="index-portability-142"></a> +<!-- =========> --> + + </body></html> +