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| 22 | <title>Complex Data Types (GNU C Language Manual)</title>
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| 31 | <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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| 32 | <link href="Primitive-Types.html" rel="up" title="Primitive Types">
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| 55 | </head>
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| 56 |
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| 57 | <body lang="en">
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| 58 | <span id="Complex-Data-Types"></span><div class="header">
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| 59 | <p>
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| 60 | Next: <a href="The-Void-Type.html" accesskey="n" rel="next">The Void Type</a>, Previous: <a href="Floating_002dPoint-Data-Types.html" accesskey="p" rel="prev">Floating-Point Data Types</a>, Up: <a href="Primitive-Types.html" accesskey="u" rel="up">Primitive Types</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Symbol-Index.html" title="Index" rel="index">Index</a>]</p>
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| 61 | </div>
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| 62 | <hr>
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| 63 | <span id="Complex-Data-Types-1"></span><h3 class="section">11.3 Complex Data Types</h3>
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| 64 | <span id="index-complex-numbers"></span>
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| 65 | <span id="index-types_002c-complex"></span>
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| 66 | <span id="index-_005fComplex-keyword"></span>
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| 67 | <span id="index-_005f_005fcomplex_005f_005f-keyword"></span>
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| 68 | <span id="index-_005fComplex"></span>
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| 69 | <span id="index-_005f_005fcomplex_005f_005f"></span>
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| 70 |
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| 71 | <p>Complex numbers can include both a real part and an imaginary part.
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| 72 | The numeric constants covered above have real-numbered values. An
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| 73 | imaginary-valued constant is an ordinary real-valued constant followed
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| 74 | by ‘<samp>i</samp>’.
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| 75 | </p>
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| 76 | <p>To declare numeric variables as complex, use the <code>_Complex</code>
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| 77 | keyword.<a id="DOCF4" href="#FOOT4"><sup>4</sup></a> The
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| 78 | standard C complex data types are floating point,
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| 79 | </p>
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| 80 | <div class="example">
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| 81 | <pre class="example">_Complex float foo;
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| 82 | _Complex double bar;
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| 83 | _Complex long double quux;
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| 84 | </pre></div>
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| 85 |
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| 86 | <p>but GNU C supports integer complex types as well.
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| 87 | </p>
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| 88 | <p>Since <code>_Complex</code> is a keyword just like <code>float</code> and
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| 89 | <code>double</code> and <code>long</code>, the keywords can appear in any order,
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| 90 | but the order shown above seems most logical.
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| 91 | </p>
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| 92 | <p>GNU C supports constants for complex values; for instance, <code>4.0 +
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| 93 | 3.0i</code> has the value 4 + 3i as type <code>_Complex double</code>.
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| 94 | See <a href="Imaginary-Constants.html">Imaginary Constants</a>.
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| 95 | </p>
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| 96 | <p>To pull the real and imaginary parts of the number back out, GNU C
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| 97 | provides the keywords <code>__real__</code> and <code>__imag__</code>:
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| 98 | </p>
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| 99 | <div class="example">
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| 100 | <pre class="example">_Complex double foo = 4.0 + 3.0i;
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| 101 |
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| 102 | double a = __real__ foo; /* <span class="roman"><code>a</code> is now 4.0.</span> */
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| 103 | double b = __imag__ foo; /* <span class="roman"><code>b</code> is now 3.0.</span> */
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| 104 | </pre></div>
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| 105 |
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| 106 | <p>Standard C does not include these keywords, and instead relies on
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| 107 | functions defined in <code>complex.h</code> for accessing the real and
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| 108 | imaginary parts of a complex number: <code>crealf</code>, <code>creal</code>, and
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| 109 | <code>creall</code> extract the real part of a float, double, or long double
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| 110 | complex number, respectively; <code>cimagf</code>, <code>cimag</code>, and
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| 111 | <code>cimagl</code> extract the imaginary part.
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| 112 | </p>
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| 113 | <span id="index-complex-conjugation"></span>
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| 114 | <p>GNU C also defines ‘<samp>~</samp>’ as an operator for complex conjugation,
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| 115 | which means negating the imaginary part of a complex number:
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| 116 | </p>
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| 117 | <div class="example">
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| 118 | <pre class="example">_Complex double foo = 4.0 + 3.0i;
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| 119 | _Complex double bar = ~foo; /* <span class="roman"><code>bar</code> is now 4 - 3i.</span> */
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| 120 | </pre></div>
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| 121 |
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| 122 | <p>For standard C compatibility, you can use the appropriate library
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| 123 | function: <code>conjf</code>, <code>conj</code>, or <code>confl</code>.
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| 124 | </p>
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| 125 | <div class="footnote">
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| 126 | <hr>
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| 127 | <h4 class="footnotes-heading">Footnotes</h4>
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| 128 |
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| 129 | <h5><a id="FOOT4" href="#DOCF4">(4)</a></h3>
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| 130 | <p>For compatibility with older versions of GNU C, the
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| 131 | keyword <code>__complex__</code> is also allowed. Going forward, however,
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| 132 | use the new <code>_Complex</code> keyword as defined in ISO C11.</p>
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| 133 | </div>
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| 134 | <hr>
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| 135 | <div class="header">
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| 136 | <p>
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| 137 | Next: <a href="The-Void-Type.html" accesskey="n" rel="next">The Void Type</a>, Previous: <a href="Floating_002dPoint-Data-Types.html" accesskey="p" rel="prev">Floating-Point Data Types</a>, Up: <a href="Primitive-Types.html" accesskey="u" rel="up">Primitive Types</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Symbol-Index.html" title="Index" rel="index">Index</a>]</p>
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