diff options
Diffstat (limited to 'share/doc/gcc/Complex.html')
| -rw-r--r-- | share/doc/gcc/Complex.html | 192 |
1 files changed, 192 insertions, 0 deletions
diff --git a/share/doc/gcc/Complex.html b/share/doc/gcc/Complex.html new file mode 100644 index 0000000..4f085a3 --- /dev/null +++ b/share/doc/gcc/Complex.html @@ -0,0 +1,192 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> +<html> +<!-- This file documents the use of the GNU compilers. + +Copyright (C) 1988-2023 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 "Funding Free Software", the Front-Cover +Texts being (a) (see below), and with the Back-Cover Texts being (b) +(see below). A copy of the license is included in the section entitled +"GNU Free Documentation License". + +(a) The FSF's Front-Cover Text is: + +A GNU Manual + +(b) The FSF's Back-Cover Text is: + +You have freedom to copy and modify this GNU Manual, like GNU + software. Copies published by the Free Software Foundation raise + funds for GNU development. --> +<!-- Created by GNU Texinfo 5.1, http://www.gnu.org/software/texinfo/ --> +<head> +<title>Using the GNU Compiler Collection (GCC): Complex</title> + +<meta name="description" content="Using the GNU Compiler Collection (GCC): Complex"> +<meta name="keywords" content="Using the GNU Compiler Collection (GCC): Complex"> +<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="Indices.html#Indices" rel="index" title="Indices"> +<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents"> +<link href="C-Extensions.html#C-Extensions" rel="up" title="C Extensions"> +<link href="Floating-Types.html#Floating-Types" rel="next" title="Floating Types"> +<link href="Long-Long.html#Long-Long" rel="previous" title="Long Long"> +<style type="text/css"> +<!-- +a.summary-letter {text-decoration: none} +blockquote.smallquotation {font-size: smaller} +div.display {margin-left: 3.2em} +div.example {margin-left: 3.2em} +div.indentedblock {margin-left: 3.2em} +div.lisp {margin-left: 3.2em} +div.smalldisplay {margin-left: 3.2em} +div.smallexample {margin-left: 3.2em} +div.smallindentedblock {margin-left: 3.2em; font-size: smaller} +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.nocodebreak {white-space:nowrap} +span.nolinebreak {white-space:nowrap} +span.roman {font-family:serif; font-weight:normal} +span.sansserif {font-family:sans-serif; font-weight:normal} +ul.no-bullet {list-style: none} +--> +</style> + + +</head> + +<body lang="en_US" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000"> +<a name="Complex"></a> +<div class="header"> +<p> +Next: <a href="Floating-Types.html#Floating-Types" accesskey="n" rel="next">Floating Types</a>, Previous: <a href="Long-Long.html#Long-Long" accesskey="p" rel="previous">Long Long</a>, Up: <a href="C-Extensions.html#C-Extensions" accesskey="u" rel="up">C Extensions</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Indices.html#Indices" title="Index" rel="index">Index</a>]</p> +</div> +<hr> +<a name="Complex-Numbers"></a> +<h3 class="section">6.11 Complex Numbers</h3> +<a name="index-complex-numbers"></a> +<a name="index-_005fComplex-keyword"></a> +<a name="index-_005f_005fcomplex_005f_005f-keyword"></a> + +<p>ISO C99 supports complex floating data types, and as an extension GCC +supports them in C90 mode and in C++. GCC also supports complex integer data +types which are not part of ISO C99. You can declare complex types +using the keyword <code>_Complex</code>. As an extension, the older GNU +keyword <code>__complex__</code> is also supported. +</p> +<p>For example, ‘<samp>_Complex double x;</samp>’ declares <code>x</code> as a +variable whose real part and imaginary part are both of type +<code>double</code>. ‘<samp>_Complex short int y;</samp>’ declares <code>y</code> to +have real and imaginary parts of type <code>short int</code>; this is not +likely to be useful, but it shows that the set of complex types is +complete. +</p> +<p>To write a constant with a complex data type, use the suffix ‘<samp>i</samp>’ or +‘<samp>j</samp>’ (either one; they are equivalent). For example, <code>2.5fi</code> +has type <code>_Complex float</code> and <code>3i</code> has type +<code>_Complex int</code>. Such a constant always has a pure imaginary +value, but you can form any complex value you like by adding one to a +real constant. This is a GNU extension; if you have an ISO C99 +conforming C library (such as the GNU C Library), and want to construct complex +constants of floating type, you should include <code><complex.h></code> and +use the macros <code>I</code> or <code>_Complex_I</code> instead. +</p> +<p>The ISO C++14 library also defines the ‘<samp>i</samp>’ suffix, so C++14 code +that includes the ‘<samp><complex></samp>’ header cannot use ‘<samp>i</samp>’ for the +GNU extension. The ‘<samp>j</samp>’ suffix still has the GNU meaning. +</p> +<p>GCC can handle both implicit and explicit casts between the <code>_Complex</code> +types and other <code>_Complex</code> types as casting both the real and imaginary +parts to the scalar type. +GCC can handle implicit and explicit casts from a scalar type to a <code>_Complex</code> +type and where the imaginary part will be considered zero. +The C front-end can handle implicit and explicit casts from a <code>_Complex</code> type +to a scalar type where the imaginary part will be ignored. In C++ code, this cast +is considered illformed and G++ will error out. +</p> +<p>GCC provides a built-in function <code>__builtin_complex</code> will can be used to +construct a complex value. +</p> +<a name="index-_005f_005freal_005f_005f-keyword"></a> +<a name="index-_005f_005fimag_005f_005f-keyword"></a> + +<p>GCC has a few extensions which can be used to extract the real +and the imaginary part of the complex-valued expression. Note +these expressions are lvalues if the <var>exp</var> is an lvalue. +These expressions operands have the type of a complex type +which might get prompoted to a complex type from a scalar type. +E.g. <code>__real__ (int)<var>x</var></code> is the same as casting to +<code>_Complex int</code> before <code>__real__</code> is done. +</p> +<table> +<thead><tr><th width="40%">Expression</th><th width="60%">Description</th></tr></thead> +<tr><td width="40%"><code>__real__ <var>exp</var></code></td><td width="60%">Extract the real part of <var>exp</var>.</td></tr> +<tr><td width="40%"><code>__imag__ <var>exp</var></code></td><td width="60%">Extract the imaginary part of <var>exp</var>.</td></tr> +</table> + +<p>For values of floating point, you should use the ISO C99 +functions, declared in <code><complex.h></code> and also provided as +built-in functions by GCC. +</p> +<table> +<thead><tr><th width="40%">Expression</th><th width="20%">float</th><th width="20%">double</th><th width="20%">long double</th></tr></thead> +<tr><td width="40%"><code>__real__ <var>exp</var></code></td><td width="20%"><code>crealf</code></td><td width="20%"><code>creal</code></td><td width="20%"><code>creall</code></td></tr> +<tr><td width="40%"><code>__imag__ <var>exp</var></code></td><td width="20%"><code>cimagf</code></td><td width="20%"><code>cimag</code></td><td width="20%"><code>cimagl</code></td></tr> +</table> + +<a name="index-complex-conjugation"></a> +<p>The operator ‘<samp>~</samp>’ performs complex conjugation when used on a value +with a complex type. This is a GNU extension; for values of +floating type, you should use the ISO C99 functions <code>conjf</code>, +<code>conj</code> and <code>conjl</code>, declared in <code><complex.h></code> and also +provided as built-in functions by GCC. Note unlike the <code>__real__</code> +and <code>__imag__</code> operators, this operator will not do an implicit cast +to the complex type because the ‘<samp>~</samp>’ is already a normal operator. +</p> +<p>GCC can allocate complex automatic variables in a noncontiguous +fashion; it’s even possible for the real part to be in a register while +the imaginary part is on the stack (or vice versa). Only the DWARF +debug info format can represent this, so use of DWARF is recommended. +If you are using the stabs debug info format, GCC describes a noncontiguous +complex variable as if it were two separate variables of noncomplex type. +If the variable’s actual name is <code>foo</code>, the two fictitious +variables are named <code>foo$real</code> and <code>foo$imag</code>. You can +examine and set these two fictitious variables with your debugger. +</p> +<dl> +<dt><a name="index-_005f_005fbuiltin_005fcomplex"></a>Built-in Function: <em><var>type</var></em> <strong>__builtin_complex</strong> <em>(<var>real</var>, <var>imag</var>)</em></dt> +<dd> +<p>The built-in function <code>__builtin_complex</code> is provided for use in +implementing the ISO C11 macros <code>CMPLXF</code>, <code>CMPLX</code> and +<code>CMPLXL</code>. <var>real</var> and <var>imag</var> must have the same type, a +real binary floating-point type, and the result has the corresponding +complex type with real and imaginary parts <var>real</var> and <var>imag</var>. +Unlike ‘<samp><var>real</var> + I * <var>imag</var></samp>’, this works even when +infinities, NaNs and negative zeros are involved. +</p> +</dd></dl> + +<hr> +<div class="header"> +<p> +Next: <a href="Floating-Types.html#Floating-Types" accesskey="n" rel="next">Floating Types</a>, Previous: <a href="Long-Long.html#Long-Long" accesskey="p" rel="previous">Long Long</a>, Up: <a href="C-Extensions.html#C-Extensions" accesskey="u" rel="up">C Extensions</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Indices.html#Indices" title="Index" rel="index">Index</a>]</p> +</div> + + + +</body> +</html> |