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57
58<h3 class="section">6.10 Complex Numbers</h3>
59
60<p><a name="index-complex-numbers-2281"></a><a name="index-g_t_0040code_007b_005fComplex_007d-keyword-2282"></a><a name="index-g_t_0040code_007b_005f_005fcomplex_005f_005f_007d-keyword-2283"></a>
61ISO C99 supports complex floating data types, and as an extension GCC
62supports them in C90 mode and in C++, and supports complex integer data
63types which are not part of ISO C99.  You can declare complex types
64using the keyword <code>_Complex</code>.  As an extension, the older GNU
65keyword <code>__complex__</code> is also supported.
66
67 <p>For example, &lsquo;<samp><span class="samp">_Complex double x;</span></samp>&rsquo; declares <code>x</code> as a
68variable whose real part and imaginary part are both of type
69<code>double</code>.  &lsquo;<samp><span class="samp">_Complex short int y;</span></samp>&rsquo; declares <code>y</code> to
70have real and imaginary parts of type <code>short int</code>; this is not
71likely to be useful, but it shows that the set of complex types is
72complete.
73
74 <p>To write a constant with a complex data type, use the suffix &lsquo;<samp><span class="samp">i</span></samp>&rsquo; or
75&lsquo;<samp><span class="samp">j</span></samp>&rsquo; (either one; they are equivalent).  For example, <code>2.5fi</code>
76has type <code>_Complex float</code> and <code>3i</code> has type
77<code>_Complex int</code>.  Such a constant always has a pure imaginary
78value, but you can form any complex value you like by adding one to a
79real constant.  This is a GNU extension; if you have an ISO C99
80conforming C library (such as GNU libc), and want to construct complex
81constants of floating type, you should include <code>&lt;complex.h&gt;</code> and
82use the macros <code>I</code> or <code>_Complex_I</code> instead.
83
84 <p><a name="index-g_t_0040code_007b_005f_005freal_005f_005f_007d-keyword-2284"></a><a name="index-g_t_0040code_007b_005f_005fimag_005f_005f_007d-keyword-2285"></a>To extract the real part of a complex-valued expression <var>exp</var>, write
85<code>__real__ </code><var>exp</var>.  Likewise, use <code>__imag__</code> to
86extract the imaginary part.  This is a GNU extension; for values of
87floating type, you should use the ISO C99 functions <code>crealf</code>,
88<code>creal</code>, <code>creall</code>, <code>cimagf</code>, <code>cimag</code> and
89<code>cimagl</code>, declared in <code>&lt;complex.h&gt;</code> and also provided as
90built-in functions by GCC.
91
92 <p><a name="index-complex-conjugation-2286"></a>The operator &lsquo;<samp><span class="samp">~</span></samp>&rsquo; performs complex conjugation when used on a value
93with a complex type.  This is a GNU extension; for values of
94floating type, you should use the ISO C99 functions <code>conjf</code>,
95<code>conj</code> and <code>conjl</code>, declared in <code>&lt;complex.h&gt;</code> and also
96provided as built-in functions by GCC.
97
98 <p>GCC can allocate complex automatic variables in a noncontiguous
99fashion; it's even possible for the real part to be in a register while
100the imaginary part is on the stack (or vice-versa).  Only the DWARF2
101debug info format can represent this, so use of DWARF2 is recommended. 
102If you are using the stabs debug info format, GCC describes a noncontiguous
103complex variable as if it were two separate variables of noncomplex type. 
104If the variable's actual name is <code>foo</code>, the two fictitious
105variables are named <code>foo$real</code> and <code>foo$imag</code>.  You can
106examine and set these two fictitious variables with your debugger.
107
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