| <html lang="en"> |
| <head> |
| <title>Complex Numbers - The GNU C Library</title> |
| <meta http-equiv="Content-Type" content="text/html"> |
| <meta name="description" content="The GNU C Library"> |
| <meta name="generator" content="makeinfo 4.13"> |
| <link title="Top" rel="start" href="index.html#Top"> |
| <link rel="up" href="Arithmetic.html#Arithmetic" title="Arithmetic"> |
| <link rel="prev" href="Arithmetic-Functions.html#Arithmetic-Functions" title="Arithmetic Functions"> |
| <link rel="next" href="Operations-on-Complex.html#Operations-on-Complex" title="Operations on Complex"> |
| <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage"> |
| <!-- |
| This file documents the GNU C library. |
| |
| This is Edition 0.12, last updated 2007-10-27, |
| of `The GNU C Library Reference Manual', for version |
| 2.8 (Sourcery G++ Lite 2011.03-41). |
| |
| Copyright (C) 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2001, 2002, |
| 2003, 2007, 2008, 2010 Free Software Foundation, Inc. |
| |
| Permission is granted to copy, distribute and/or modify this document |
| under the terms of the GNU Free Documentation License, Version 1.3 or |
| any later version published by the Free Software Foundation; with the |
| Invariant Sections being ``Free Software Needs Free Documentation'' |
| and ``GNU Lesser General Public License'', the Front-Cover texts being |
| ``A GNU Manual'', and with the Back-Cover Texts as in (a) below. A |
| copy of the license is included in the section entitled "GNU Free |
| Documentation License". |
| |
| (a) The FSF's Back-Cover Text is: ``You have the freedom to |
| copy and modify this GNU manual. Buying copies from the FSF |
| supports it in developing GNU and promoting software freedom.''--> |
| <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> |
| <link rel="stylesheet" type="text/css" href="../cs.css"> |
| </head> |
| <body> |
| <div class="node"> |
| <a name="Complex-Numbers"></a> |
| <p> |
| Next: <a rel="next" accesskey="n" href="Operations-on-Complex.html#Operations-on-Complex">Operations on Complex</a>, |
| Previous: <a rel="previous" accesskey="p" href="Arithmetic-Functions.html#Arithmetic-Functions">Arithmetic Functions</a>, |
| Up: <a rel="up" accesskey="u" href="Arithmetic.html#Arithmetic">Arithmetic</a> |
| <hr> |
| </div> |
| |
| <h3 class="section">20.9 Complex Numbers</h3> |
| |
| <p><a name="index-complex_002eh-2521"></a><a name="index-complex-numbers-2522"></a> |
| ISO C99<!-- /@w --> introduces support for complex numbers in C. This is done |
| with a new type qualifier, <code>complex</code>. It is a keyword if and only |
| if <samp><span class="file">complex.h</span></samp> has been included. There are three complex types, |
| corresponding to the three real types: <code>float complex</code>, |
| <code>double complex</code>, and <code>long double complex</code>. |
| |
| <p>To construct complex numbers you need a way to indicate the imaginary |
| part of a number. There is no standard notation for an imaginary |
| floating point constant. Instead, <samp><span class="file">complex.h</span></samp> defines two macros |
| that can be used to create complex numbers. |
| |
| <div class="defun"> |
| — Macro: const float complex <b>_Complex_I</b><var><a name="index-g_t_005fComplex_005fI-2523"></a></var><br> |
| <blockquote><p>This macro is a representation of the complex number “0+1i”. |
| Multiplying a real floating-point value by <code>_Complex_I</code> gives a |
| complex number whose value is purely imaginary. You can use this to |
| construct complex constants: |
| |
| <pre class="smallexample"> 3.0 + 4.0i = <code>3.0 + 4.0 * _Complex_I</code> |
| </pre> |
| <p>Note that <code>_Complex_I * _Complex_I</code> has the value <code>-1</code>, but |
| the type of that value is <code>complex</code>. |
| </p></blockquote></div> |
| |
| <!-- Put this back in when gcc supports _Imaginary_I. It's too confusing. --> |
| <p class="noindent"><code>_Complex_I</code> is a bit of a mouthful. <samp><span class="file">complex.h</span></samp> also defines |
| a shorter name for the same constant. |
| |
| <div class="defun"> |
| — Macro: const float complex <b>I</b><var><a name="index-I-2524"></a></var><br> |
| <blockquote><p>This macro has exactly the same value as <code>_Complex_I</code>. Most of the |
| time it is preferable. However, it causes problems if you want to use |
| the identifier <code>I</code> for something else. You can safely write |
| |
| <pre class="smallexample"> #include <complex.h> |
| #undef I |
| </pre> |
| <p class="noindent">if you need <code>I</code> for your own purposes. (In that case we recommend |
| you also define some other short name for <code>_Complex_I</code>, such as |
| <code>J</code>.) |
| |
| </blockquote></div> |
| |
| </body></html> |
| |
