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| 22 | <title>Floating Representations (GNU C Language Manual)</title>
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| 30 | <link href="Symbol-Index.html" rel="index" title="Symbol Index">
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| 31 | <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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| 32 | <link href="Floating-Point-in-Depth.html" rel="up" title="Floating Point in Depth">
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| 57 | <body lang="en">
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| 58 | <span id="Floating-Representations"></span><div class="header">
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| 59 | <p>
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| 60 | Next: <a href="Floating-Type-Specs.html" accesskey="n" rel="next">Floating Type Specs</a>, Up: <a href="Floating-Point-in-Depth.html" accesskey="u" rel="up">Floating Point in Depth</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="Floating_002dPoint-Representations"></span><h3 class="section">28.1 Floating-Point Representations</h3>
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| 64 | <span id="index-floating_002dpoint-representations"></span>
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| 65 | <span id="index-representation-of-floating_002dpoint-numbers"></span>
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| 66 |
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| 67 | <span id="index-IEEE-754_002d2008-Standard"></span>
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| 68 | <p>Storing numbers as <em>floating point</em> allows representation of
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| 69 | numbers with fractional values, in a range larger than that of
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| 70 | hardware integers. A floating-point number consists of a sign bit, a
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| 71 | <em>significand</em> (also called the <em>mantissa</em>), and a power of a
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| 72 | fixed base. GNU C uses the floating-point representations specified by
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| 73 | the <cite>IEEE 754-2008 Standard for Floating-Point Arithmetic</cite>.
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| 74 | </p>
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| 75 | <p>The IEEE 754-2008 specification defines basic binary floating-point
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| 76 | formats of five different sizes: 16-bit, 32-bit, 64-bit, 128-bit, and
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| 77 | 256-bit. The formats of 32, 64, and 128 bits are used for the
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| 78 | standard C types <code>float</code>, <code>double</code>, and <code>long double</code>.
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| 79 | GNU C supports the 16-bit floating point type <code>_Float16</code> on some
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| 80 | platforms, but does not support the 256-bit floating point type.
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| 81 | </p>
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| 82 | <p>Each of the formats encodes the floating-point number as a sign bit.
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| 83 | After this comes an exponent that specifies a power of 2 (with a fixed
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| 84 | offset). Then comes the significand.
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| 85 | </p>
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| 86 | <p>The first bit of the significand, before the binary point, is always
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| 87 | 1, so there is no need to store it in memory. It is called the
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| 88 | <em>hidden bit</em> because it doesn’t appear in the floating-point
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| 89 | number as used in the computer itself.
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| 90 | </p>
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| 91 | <p>All of those floating-point formats are sign-magnitude representations,
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| 92 | so +0 and -0 are different values.
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| 93 | </p>
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| 94 | <p>Besides the IEEE 754 format 128-bit float, GNU C also offers a format
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| 95 | consisting of a pair of 64-bit floating point numbers. This lacks the
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| 96 | full exponent range of the IEEE 128-bit format, but is useful when the
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| 97 | underlying hardware platform does not support that.
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| 98 | </p>
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| 99 |
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| 100 |
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| 101 |
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