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| 58 | <span id="Rounding-Control"></span><div class="header">
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| 59 | <p>
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| 60 | Next: <a href="Machine-Epsilon.html" accesskey="n" rel="next">Machine Epsilon</a>, Previous: <a href="Scaling-by-the-Base.html" accesskey="p" rel="prev">Scaling by the Base</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="Rounding-Control-1"></span><h3 class="section">28.17 Rounding Control</h3>
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| 64 | <span id="index-rounding-control-_0028floating-point_0029"></span>
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| 65 | <span id="index-floating_002dpoint-rounding-control"></span>
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| 66 |
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| 67 | <p>Here we describe how to specify the rounding mode at run time. System
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| 68 | header file <samp>fenv.h</samp> provides the prototypes for these functions.
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| 69 | See <a href="https://www.gnu.org/software/libc/manual/html_node/Rounding.html#Rounding">Rounding</a> in <cite>The GNU C Library Reference Manual</cite>.
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| 70 | </p>
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| 71 | <p>That header file also provides constant names for the four rounding modes:
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| 72 | <code>FE_DOWNWARD</code>, <code>FE_TONEAREST</code>, <code>FE_TOWARDZERO</code>, and
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| 73 | <code>FE_UPWARD</code>.
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| 74 | </p>
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| 75 | <p>The function <code>fegetround</code> examines and returns the current
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| 76 | rounding mode. On a platform with IEEE 754 floating point,
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| 77 | the value will always equal one of those four constants.
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| 78 | On other platforms, it may return a negative value. The function
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| 79 | <code>fesetround</code> sets the current rounding mode.
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| 80 | </p>
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| 81 | <p>Changing the rounding mode can be slow, so it is useful to minimize
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| 82 | the number of changes. For interval arithmetic, we seem to need three
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| 83 | changes for each operation, but we really only need two, because we
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| 84 | can write code like this example for interval addition of two reals:
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| 85 | </p>
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| 86 | <div class="example">
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| 87 | <pre class="example">{
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| 88 | struct interval_double
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| 89 | {
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| 90 | double hi, lo;
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| 91 | } v;
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| 92 | volatile double x, y;
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| 93 | int rule;
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| 94 |
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| 95 | rule = fegetround ();
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| 96 |
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| 97 | if (fesetround (FE_UPWARD) == 0)
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| 98 | {
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| 99 | v.hi = x + y;
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| 100 | v.lo = -(-x - y);
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| 101 | }
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| 102 | else
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| 103 | fatal ("ERROR: failed to change rounding rule");
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| 104 |
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| 105 | if (fesetround (rule) != 0)
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| 106 | fatal ("ERROR: failed to restore rounding rule");
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| 107 | }
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| 108 | </pre></div>
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| 109 |
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| 110 | <p>The <code>volatile</code> qualifier (see <a href="volatile.html">volatile</a>) is essential on x86
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| 111 | platforms to prevent an optimizing compiler from producing the same
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| 112 | value for both bounds.
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| 113 | </p>
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| 114 |
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