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| 22 | <title>Special Float Values (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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| 33 | <link href="Invalid-Optimizations.html" rel="next" title="Invalid Optimizations">
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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="Special-Float-Values"></span><div class="header">
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| 59 | <p>
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| 60 | Next: <a href="Invalid-Optimizations.html" accesskey="n" rel="next">Invalid Optimizations</a>, Previous: <a href="Floating-Type-Specs.html" accesskey="p" rel="prev">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="Special-Floating_002dPoint-Values"></span><h3 class="section">28.3 Special Floating-Point Values</h3>
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| 64 | <span id="index-special-floating_002dpoint-values"></span>
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| 65 | <span id="index-floating_002dpoint-values_002c-special"></span>
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| 66 |
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| 67 | <p>IEEE floating point provides for special values that are not ordinary
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| 68 | numbers.
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| 69 | </p>
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| 70 | <dl compact="compact">
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| 71 | <dt>infinities</dt>
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| 72 | <dd><p><code>+Infinity</code> and <code>-Infinity</code> are two different infinite
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| 73 | values, one positive and one negative. These result from
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| 74 | operations such as <code>1 / 0</code>, <code>Infinity + Infinity</code>,
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| 75 | <code>Infinity * Infinity</code>, and <code>Infinity + <var>finite</var></code>, and also
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| 76 | from a result that is finite, but larger than the most positive possible
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| 77 | value or smaller than the most negative possible value.
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| 78 | </p>
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| 79 | <p>See <a href="Handling-Infinity.html">Handling Infinity</a>, for more about working with infinities.
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| 80 | </p>
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| 81 | </dd>
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| 82 | <dt>NaNs (not a number)</dt>
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| 83 | <dd><span id="index-QNaN"></span>
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| 84 | <span id="index-SNaN"></span>
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| 85 | <p>There are two special values, called Not-a-Number (NaN): a quiet
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| 86 | NaN (QNaN), and a signaling NaN (SNaN).
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| 87 | </p>
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| 88 | <p>A QNaN is produced by operations for which the value is undefined
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| 89 | in real arithmetic, such as <code>0 / 0</code>, <code>sqrt (-1)</code>,
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| 90 | <code>Infinity - Infinity</code>, and any basic operation in which an
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| 91 | operand is a QNaN.
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| 92 | </p>
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| 93 | <p>The signaling NaN is intended for initializing
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| 94 | otherwise-unassigned storage, and the goal is that unlike a
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| 95 | QNaN, an SNaN <em>does</em> cause an interrupt that can be caught
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| 96 | by a software handler, diagnosed, and reported. In practice,
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| 97 | little use has been made of signaling NaNs, because the most
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| 98 | common CPUs in desktop and portable computers fail to implement
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| 99 | the full IEEE 754 Standard, and supply only one kind of NaN, the
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| 100 | quiet one. Also, programming-language standards have taken
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| 101 | decades to catch up to the IEEE 754 standard, and implementations
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| 102 | of those language standards make an additional delay before
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| 103 | programmers become willing to use these features.
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| 104 | </p>
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| 105 | <p>To enable support for signaling NaNs, use the GCC command-line option
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| 106 | <samp>-fsignaling-nans</samp>, but this is an experimental feature and may
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| 107 | not work as expected in every situation.
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| 108 | </p>
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| 109 | <p>A NaN has a sign bit, but its value means nothing.
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| 110 | </p>
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| 111 | <p>See <a href="Handling-NaN.html">Handling NaN</a>, for more about working with NaNs.
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| 112 | </p>
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| 113 | </dd>
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| 114 | <dt>subnormal numbers</dt>
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| 115 | <dd><span id="index-subnormal-numbers"></span>
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| 116 | <span id="index-underflow_002c-floating"></span>
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| 117 | <span id="index-floating-underflow"></span>
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| 118 | <span id="subnormal-numbers"></span><p>It can happen that a computed floating-point value is too small to
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| 119 | represent, such as when two tiny numbers are multiplied. The result
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| 120 | is then said to <em>underflow</em>. The traditional behavior before
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| 121 | the IEEE 754 Standard was to use zero as the result, and possibly to report
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| 122 | the underflow in some sort of program output.
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| 123 | </p>
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| 124 | <p>The IEEE 754 Standard is vague about whether rounding happens
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| 125 | before detection of floating underflow and overflow, or after, and CPU
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| 126 | designers may choose either.
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| 127 | </p>
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| 128 | <p>However, the Standard does something unusual compared to earlier
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| 129 | designs, and that is that when the result is smaller than the
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| 130 | smallest <em>normalized</em> representable value (i.e., one in
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| 131 | which the leading significand bit is <code>1</code>), the normalization
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| 132 | requirement is relaxed, leading zero bits are permitted, and
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| 133 | precision is gradually lost until there are no more bits in the
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| 134 | significand. That phenomenon is called <em>gradual underflow</em>,
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| 135 | and it serves important numerical purposes, although it does
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| 136 | reduce the precision of the final result. Some floating-point
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| 137 | designs allow you to choose at compile time, or even at
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| 138 | run time, whether underflows are gradual, or are flushed abruptly
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| 139 | to zero. Numbers that have entered the region of gradual
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| 140 | underflow are called <em>subnormal</em>.
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| 141 | </p>
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| 142 | <p>You can use the library functions <code>fesetround</code> and
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| 143 | <code>fegetround</code> to set and get the rounding mode. Rounding modes
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| 144 | are defined (if supported by the platform) in <code>fenv.h</code> as:
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| 145 | <code>FE_UPWARD</code> to round toward positive infinity; <code>FE_DOWNWARD</code>
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| 146 | to round toward negative infinity; <code>FE_TOWARDZERO</code> to round
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| 147 | toward zero; and <code>FE_TONEAREST</code> to round to the nearest
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| 148 | representable value, the default mode. It is best to use
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| 149 | <code>FE_TONEAREST</code> except when there is a special need for some other
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| 150 | mode.
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| 151 | </p></dd>
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| 152 | </dl>
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| 153 |
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| 154 | <hr>
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| 155 | <div class="header">
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| 156 | <p>
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| 157 | Next: <a href="Invalid-Optimizations.html" accesskey="n" rel="next">Invalid Optimizations</a>, Previous: <a href="Floating-Type-Specs.html" accesskey="p" rel="prev">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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| 158 | </div>
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