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<link rel="up" href="../fp_facets.html" title="Facets for Floating-Point Infinities and NaNs">
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<a accesskey="p" href="../fp_facets.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../fp_facets.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="reference.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="math_toolkit.fp_facets.facets_intro"></a><a class="link" href="facets_intro.html" title="Introduction">Introduction</a>
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</h3></div></div></div>
|
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<h6>
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<a name="math_toolkit.fp_facets.facets_intro.h0"></a>
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<span class="phrase"><a name="math_toolkit.fp_facets.facets_intro.the_problem"></a></span><a class="link" href="facets_intro.html#math_toolkit.fp_facets.facets_intro.the_problem">The
|
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Problem</a>
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</h6>
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<p>
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The C++98 standard does not specify how <span class="emphasis"><em>infinity</em></span> and
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<span class="emphasis"><em>NaN</em></span> are represented in text streams. As a result, different
|
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platforms use different string representations. This can cause undefined
|
||
behavior when text files are moved between different platforms. Some platforms
|
||
cannot even input parse their own output! So 'route-tripping' or loopback
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of output to input is not possible. For instance, the following test fails
|
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with MSVC:
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</p>
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<pre class="programlisting"><span class="identifier">stringstream</span> <span class="identifier">ss</span><span class="special">;</span>
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<span class="keyword">double</span> <span class="identifier">inf</span> <span class="special">=</span> <span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">infinity</span><span class="special">();</span>
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<span class="keyword">double</span> <span class="identifier">r</span><span class="special">;</span>
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<span class="identifier">ss</span> <span class="special"><<</span> <span class="identifier">inf</span><span class="special">;</span> <span class="comment">// Write out.</span>
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<span class="identifier">ss</span> <span class="special">>></span> <span class="identifier">r</span><span class="special">;</span> <span class="comment">// Read back in.</span>
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<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"infinity output was "</span> <span class="special"><<</span> <span class="identifier">inf</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 1.#INF</span>
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<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"infinity input was "</span> <span class="special"><<</span> <span class="identifier">r</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 1</span>
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<span class="identifier">assert</span><span class="special">(</span><span class="identifier">inf</span> <span class="special">==</span> <span class="identifier">y</span><span class="special">);</span> <span class="comment">// Fails!</span>
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</pre>
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<h6>
|
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<a name="math_toolkit.fp_facets.facets_intro.h1"></a>
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<span class="phrase"><a name="math_toolkit.fp_facets.facets_intro.the_solution"></a></span><a class="link" href="facets_intro.html#math_toolkit.fp_facets.facets_intro.the_solution">The
|
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Solution</a>
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</h6>
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<p>
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The facets <code class="computeroutput"><span class="identifier">nonfinite_num_put</span></code>
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and <code class="computeroutput"><span class="identifier">nonfinite_num_get</span></code> format
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and parse all floating-point numbers, including <code class="computeroutput"><span class="identifier">infinity</span></code>
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and <code class="computeroutput"><span class="identifier">NaN</span></code>, in a consistent
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and portable manner.
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||
</p>
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<p>
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The following test succeeds with MSVC.
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||
</p>
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<pre class="programlisting"><span class="identifier">locale</span> <span class="identifier">old_locale</span><span class="special">;</span>
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||
<span class="identifier">locale</span> <span class="identifier">tmp_locale</span><span class="special">(</span><span class="identifier">old_locale</span><span class="special">,</span> <span class="keyword">new</span> <span class="identifier">nonfinite_num_put</span><span class="special"><</span><span class="keyword">char</span><span class="special">>);</span>
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<span class="identifier">locale</span> <span class="identifier">new_locale</span><span class="special">(</span><span class="identifier">tmp_locale</span><span class="special">,</span> <span class="keyword">new</span> <span class="identifier">nonfinite_num_get</span><span class="special"><</span><span class="keyword">char</span><span class="special">>);</span>
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</pre>
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<div class="tip"><table border="0" summary="Tip">
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<tr>
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<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../../doc/src/images/tip.png"></td>
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<th align="left">Tip</th>
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</tr>
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<tr><td align="left" valign="top">
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<p>
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To add two facets, <code class="computeroutput"><span class="identifier">nonfinite_num_put</span></code>
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and <code class="computeroutput"><span class="identifier">nonfinite_num_get</span></code>,
|
||
you may have to add one at a time, using a temporary locale.
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||
</p>
|
||
<p>
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||
Or you can create a new locale in one step
|
||
</p>
|
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<p>
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<code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">locale</span> <span class="identifier">new_locale</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">locale</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">locale</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">locale</span><span class="special">(),</span> <span class="keyword">new</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">nonfinite_num_put</span><span class="special"><</span><span class="keyword">char</span><span class="special">>),</span> <span class="keyword">new</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">nonfinite_num_get</span><span class="special"><</span><span class="keyword">char</span><span class="special">>));</span></code>
|
||
</p>
|
||
<p>
|
||
and, for example, use it to imbue an input and output stringstream.
|
||
</p>
|
||
</td></tr>
|
||
</table></div>
|
||
<div class="tip"><table border="0" summary="Tip">
|
||
<tr>
|
||
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../../doc/src/images/tip.png"></td>
|
||
<th align="left">Tip</th>
|
||
</tr>
|
||
<tr><td align="left" valign="top"><p>
|
||
To just change an input or output stream, you can concisely write <code class="computeroutput"><span class="identifier">cout</span><span class="special">.</span><span class="identifier">imbue</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">locale</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">locale</span><span class="special">(),</span> <span class="keyword">new</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">nonfinite_num_put</span><span class="special"><</span><span class="keyword">char</span><span class="special">>));</span></code> or <code class="computeroutput"><span class="identifier">cin</span><span class="special">.</span><span class="identifier">imbue</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">locale</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">locale</span><span class="special">(),</span> <span class="keyword">new</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">nonfinite_num_get</span><span class="special"><</span><span class="keyword">char</span><span class="special">>));</span></code>
|
||
</p></td></tr>
|
||
</table></div>
|
||
<pre class="programlisting"><span class="identifier">stringstream</span> <span class="identifier">ss</span><span class="special">;</span>
|
||
<span class="identifier">ss</span><span class="special">.</span><span class="identifier">imbue</span><span class="special">(</span><span class="identifier">new_locale</span><span class="special">);</span>
|
||
<span class="keyword">double</span> <span class="identifier">inf</span> <span class="special">=</span> <span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">infinity</span><span class="special">();</span>
|
||
<span class="identifier">ss</span> <span class="special"><<</span> <span class="identifier">inf</span><span class="special">;</span> <span class="comment">// Write out.</span>
|
||
<span class="identifier">BOOST_MATH_ASSERT</span><span class="special">(</span><span class="identifier">ss</span><span class="special">.</span><span class="identifier">str</span><span class="special">()</span> <span class="special">==</span> <span class="string">"inf"</span><span class="special">);</span>
|
||
<span class="keyword">double</span> <span class="identifier">r</span><span class="special">;</span>
|
||
<span class="identifier">ss</span> <span class="special">>></span> <span class="identifier">r</span><span class="special">;</span> <span class="comment">// Read back in.</span>
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||
<span class="identifier">BOOST_MATH_ASSERT</span><span class="special">(</span><span class="identifier">inf</span> <span class="special">==</span> <span class="identifier">r</span><span class="special">);</span> <span class="comment">// Confirms that the double values really are identical.</span>
|
||
|
||
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"infinity output was "</span> <span class="special"><<</span> <span class="identifier">ss</span><span class="special">.</span><span class="identifier">str</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
|
||
<span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"infinity input was "</span> <span class="special"><<</span> <span class="identifier">r</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
|
||
<span class="comment">// But the string representation of r displayed will be the native type</span>
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||
<span class="comment">// because, when it was constructed, cout had NOT been imbued</span>
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||
<span class="comment">// with the new locale containing the nonfinite_numput facet.</span>
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||
<span class="comment">// So the cout output will be "1.#INF on MS platforms</span>
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||
<span class="comment">// and may be "inf" or other string representation on other platforms.</span>
|
||
</pre>
|
||
<h5>
|
||
<a name="math_toolkit.fp_facets.facets_intro.h2"></a>
|
||
<span class="phrase"><a name="math_toolkit.fp_facets.facets_intro.c_0x_standard_for_output_of_infi"></a></span><a class="link" href="facets_intro.html#math_toolkit.fp_facets.facets_intro.c_0x_standard_for_output_of_infi">C++0X
|
||
standard for output of infinity and NaN</a>
|
||
</h5>
|
||
<p>
|
||
<a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2011/n3242.pdf" target="_top">C++0X
|
||
(final) draft standard</a> does not explicitly specify the representation
|
||
(and input) of nonfinite values, leaving it implementation-defined. So without
|
||
some specific action, input and output of nonfinite values is not portable.
|
||
</p>
|
||
<h5>
|
||
<a name="math_toolkit.fp_facets.facets_intro.h3"></a>
|
||
<span class="phrase"><a name="math_toolkit.fp_facets.facets_intro.c99_standard_for_output_of_infin"></a></span><a class="link" href="facets_intro.html#math_toolkit.fp_facets.facets_intro.c99_standard_for_output_of_infin">C99
|
||
standard for output of infinity and NaN</a>
|
||
</h5>
|
||
<p>
|
||
The <a href="http://www.open-std.org/JTC1/SC22/WG14/www/docs/n1256.pdf" target="_top">C99
|
||
standard</a> <span class="bold"><strong>does</strong></span> specify how infinity
|
||
and NaN are formatted by printf and similar output functions, and parsed
|
||
by scanf and similar input functions.
|
||
</p>
|
||
<p>
|
||
The following string representations are used:
|
||
</p>
|
||
<div class="table">
|
||
<a name="math_toolkit.fp_facets.facets_intro.c99_representation_of_infinity_a"></a><p class="title"><b>Table 2.1. C99 Representation of Infinity and NaN</b></p>
|
||
<div class="table-contents"><table class="table" summary="C99 Representation of Infinity and NaN">
|
||
<colgroup>
|
||
<col>
|
||
<col>
|
||
</colgroup>
|
||
<thead><tr>
|
||
<th>
|
||
<p>
|
||
number
|
||
</p>
|
||
</th>
|
||
<th>
|
||
<p>
|
||
string
|
||
</p>
|
||
</th>
|
||
</tr></thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
Positive infinity
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
"inf" or "infinity"
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
Positive NaN
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
"nan" or "nan(...)"
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
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Negative infinity
|
||
</p>
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</td>
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<td>
|
||
<p>
|
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"-inf" or "-infinity"
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<p>
|
||
Negative NaN
|
||
</p>
|
||
</td>
|
||
<td>
|
||
<p>
|
||
"-nan" or "-nan(...)"
|
||
</p>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
</div>
|
||
<br class="table-break"><p>
|
||
So following C99 provides a sensible 'standard' way of handling input and
|
||
output of nonfinites in C++, and this implementation follows most of these
|
||
formats.
|
||
</p>
|
||
<h6>
|
||
<a name="math_toolkit.fp_facets.facets_intro.h4"></a>
|
||
<span class="phrase"><a name="math_toolkit.fp_facets.facets_intro.signaling_nans"></a></span><a class="link" href="facets_intro.html#math_toolkit.fp_facets.facets_intro.signaling_nans">Signaling
|
||
NaNs</a>
|
||
</h6>
|
||
<p>
|
||
A particular type of NaN is the signaling NaN. The usual mechanism of signaling
|
||
is by raising a floating-point exception. Signaling NaNs are defined by
|
||
<a href="http://en.wikipedia.org/wiki/IEEE_floating-point_standard" target="_top">IEEE
|
||
754-2008</a>.
|
||
</p>
|
||
<p>
|
||
Floating-point values with layout <span class="emphasis"><em>s</em></span>111 1111 1<span class="emphasis"><em>a</em></span>xx
|
||
xxxx xxxx xxxx xxxx xxxx where <span class="emphasis"><em>s</em></span> is the sign, <span class="emphasis"><em>x</em></span>
|
||
is the payload, and bit <span class="emphasis"><em>a</em></span> determines the type of NaN.
|
||
</p>
|
||
<p>
|
||
If bit <span class="emphasis"><em>a</em></span> = 1, it is a quiet NaN.
|
||
</p>
|
||
<p>
|
||
If bit <span class="emphasis"><em>a</em></span> is zero and the payload <span class="emphasis"><em>x</em></span>
|
||
is nonzero, then it is a signaling NaN.
|
||
</p>
|
||
<p>
|
||
Although there has been theoretical interest in the ability of a signaling
|
||
NaN to raise an exception, for example to prevent use of an uninitialised
|
||
variable, in practice there appears to be no useful application of signaling
|
||
NaNs for most current processors. <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2011/n3242.pdf" target="_top">C++0X
|
||
18.3.2.2</a> still specifies a (implementation-defined) representation
|
||
for signaling NaN, and <code class="computeroutput"><span class="keyword">static</span> <span class="keyword">constexpr</span> <span class="keyword">bool</span> <span class="identifier">has_signaling_NaN</span></code> a method of checking
|
||
if a floating-point type has a representation for signaling NaN.
|
||
</p>
|
||
<p>
|
||
But in practice, most platforms treat signaling NaNs in the same as quiet
|
||
NaNs. So, for example, they are represented by "nan" on output
|
||
in <a href="http://www.open-std.org/JTC1/SC22/WG14/www/docs/n1256.pdf" target="_top">C99</a>
|
||
format, and output as <code class="computeroutput"><span class="number">1.</span><span class="special">#</span><span class="identifier">QNAN</span></code> by Microsoft compilers.
|
||
</p>
|
||
<div class="note"><table border="0" summary="Note">
|
||
<tr>
|
||
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/src/images/note.png"></td>
|
||
<th align="left">Note</th>
|
||
</tr>
|
||
<tr><td align="left" valign="top">
|
||
<p>
|
||
The C99 standard does not distinguish between the quiet NaN and signaling
|
||
NaN values. A quiet NaN propagates through almost every arithmetic operation
|
||
without raising a floating-point exception; a signaling NaN generally raises
|
||
a floating-point exception when occurring as an arithmetic operand.
|
||
</p>
|
||
<p>
|
||
C99 specification does not define the behavior of signaling NaNs. NaNs
|
||
created by IEC 60559 operations are always quiet. Therefore this implementation
|
||
follows C99, and treats the signaling NaN bit as just a part of the NaN
|
||
payload field. So this implementation does not distinguish between the
|
||
two classes of NaN.
|
||
</p>
|
||
</td></tr>
|
||
</table></div>
|
||
<div class="note"><table border="0" summary="Note">
|
||
<tr>
|
||
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/src/images/note.png"></td>
|
||
<th align="left">Note</th>
|
||
</tr>
|
||
<tr><td align="left" valign="top">
|
||
<p>
|
||
An implementation may give zero and non-numeric values (such as infinities
|
||
and NaNs) a sign or may leave them unsigned. Wherever such values are unsigned,
|
||
any requirement in the C99 Standard to retrieve the sign shall produce
|
||
an unspecified sign, and any requirement to set the sign shall be ignored.
|
||
</p>
|
||
<p>
|
||
This might apply to user-defined types, but in practice built-in floating-point
|
||
types <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code> and <code class="computeroutput"><span class="keyword">long</span>
|
||
<span class="keyword">double</span></code> have well-behaved signs.
|
||
</p>
|
||
</td></tr>
|
||
</table></div>
|
||
<p>
|
||
The numbers can be of type <code class="computeroutput"><span class="keyword">float</span></code>,
|
||
<code class="computeroutput"><span class="keyword">double</span></code> and <code class="computeroutput"><span class="keyword">long</span>
|
||
<span class="keyword">double</span></code>. An optional + sign can be
|
||
used with positive numbers (controlled by ios manipulator <code class="computeroutput"><span class="identifier">showpos</span></code>).
|
||
The function <code class="computeroutput"><span class="identifier">printf</span></code> and similar
|
||
C++ functions use standard formatting flags to put all lower or all upper
|
||
case (controlled by <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">ios</span></code> manipulator <code class="computeroutput"><span class="identifier">uppercase</span></code>
|
||
and <code class="computeroutput"><span class="identifier">lowercase</span></code>).
|
||
</p>
|
||
<p>
|
||
The function <code class="computeroutput"><span class="identifier">scanf</span></code> and similar
|
||
input functions are case-insensitive.
|
||
</p>
|
||
<p>
|
||
The dots in <code class="computeroutput"><span class="identifier">nan</span><span class="special">(...)</span></code>
|
||
stand for an arbitrary string. The meaning of that string is implementation
|
||
dependent. It can be used to convey extra information about the NaN, from
|
||
the 'payload'. A particular value of the payload might be used to indicate
|
||
a <span class="emphasis"><em>missing value</em></span>, for example.
|
||
</p>
|
||
<p>
|
||
This library uses the string representations specified by the C99 standard.
|
||
</p>
|
||
<p>
|
||
An example of an implementation that optionally includes the NaN payload
|
||
information is at <a href="http://publib.boulder.ibm.com/infocenter/zos/v1r10/index.jsp?topic=/com.ibm.zos.r10.bpxbd00/fprints.htm" target="_top">AIX
|
||
NaN fprintf</a>. That implementation specifies for Binary Floating Point
|
||
NANs:
|
||
</p>
|
||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
||
<li class="listitem">
|
||
A NaN ordinal sequence is a left-parenthesis character '(', followed
|
||
by a digit sequence representing an integer n, where 1 <= n <=
|
||
INT_MAX-1, followed by a right-parenthesis character ')'.
|
||
</li>
|
||
<li class="listitem">
|
||
The integer value, n, is determined by the fraction bits of the NaN argument
|
||
value as follows:
|
||
</li>
|
||
<li class="listitem">
|
||
For a signalling NaN value, NaN fraction bits are reversed (left to right)
|
||
to produce bits (right to left) of an even integer value, 2*n. Then formatted
|
||
output functions produce a (signalling) NaN ordinal sequence corresponding
|
||
to the integer value n.
|
||
</li>
|
||
<li class="listitem">
|
||
For a quiet NaN value, NaN fraction bits are reversed (left to right)
|
||
to produce bits (right to left) of an odd integer value, 2*n-1. Then
|
||
formatted output functions produce a (quiet) NaN ordinal sequence corresponding
|
||
to the integer value n.
|
||
</li>
|
||
</ul></div>
|
||
<div class="warning"><table border="0" summary="Warning">
|
||
<tr>
|
||
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Warning]" src="../../../../../../doc/src/images/warning.png"></td>
|
||
<th align="left">Warning</th>
|
||
</tr>
|
||
<tr><td align="left" valign="top"><p>
|
||
This implementation does not (yet) provide output of, or access to, the
|
||
NaN payload.
|
||
</p></td></tr>
|
||
</table></div>
|
||
</div>
|
||
<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
||
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
||
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||
Walker and Xiaogang Zhang<p>
|
||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||
</p>
|
||
</div>
|
||
<hr>
|
||
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