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  25 <div class="section">
  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.fp_facets.facets_intro"></a><a class="link" href="facets_intro.html" title="Introduction">Introduction</a>
  28 </h3></div></div></div>
  29 <h6>
  30 <a name="math_toolkit.fp_facets.facets_intro.h0"></a>
  31         <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
  32         Problem</a>
  33       </h6>
  34 <p>
  35         The C++98 standard does not specify how <span class="emphasis"><em>infinity</em></span> and
  36         <span class="emphasis"><em>NaN</em></span> are represented in text streams. As a result, different
  37         platforms use different string representations. This can cause undefined
  38         behavior when text files are moved between different platforms. Some platforms
  39         cannot even input parse their own output! So 'route-tripping' or loopback
  40         of output to input is not possible. For instance, the following test fails
  41         with MSVC:
  42       </p>
  43 <pre class="programlisting"><span class="identifier">stringstream</span> <span class="identifier">ss</span><span class="special">;</span>
  44 <span class="keyword">double</span> <span class="identifier">inf</span> <span class="special">=</span> <span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;::</span><span class="identifier">infinity</span><span class="special">();</span>
  45 <span class="keyword">double</span> <span class="identifier">r</span><span class="special">;</span>
  46 <span class="identifier">ss</span> <span class="special">&lt;&lt;</span> <span class="identifier">inf</span><span class="special">;</span> <span class="comment">// Write out.</span>
  47 <span class="identifier">ss</span> <span class="special">&gt;&gt;</span> <span class="identifier">r</span><span class="special">;</span> <span class="comment">// Read back in.</span>
  48
  49 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"infinity output was "</span> <span class="special">&lt;&lt;</span> <span class="identifier">inf</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 1.#INF</span>
  50 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"infinity input was "</span> <span class="special">&lt;&lt;</span> <span class="identifier">r</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 1</span>
  51
  52 <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>
  53 </pre>
  54 <h6>
  55 <a name="math_toolkit.fp_facets.facets_intro.h1"></a>
  56         <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
  57         Solution</a>
  58       </h6>
  59 <p>
  60         The facets <code class="computeroutput"><span class="identifier">nonfinite_num_put</span></code>
  61         and <code class="computeroutput"><span class="identifier">nonfinite_num_get</span></code> format
  62         and parse all floating-point numbers, including <code class="computeroutput"><span class="identifier">infinity</span></code>
  63         and <code class="computeroutput"><span class="identifier">NaN</span></code>, in a consistent
  64         and portable manner.
  65       </p>
  66 <p>
  67         The following test succeeds with MSVC.
  68       </p>
  69 <pre class="programlisting"><span class="identifier">locale</span> <span class="identifier">old_locale</span><span class="special">;</span>
  70 <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">&lt;</span><span class="keyword">char</span><span class="special">&gt;);</span>
  71 <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">&lt;</span><span class="keyword">char</span><span class="special">&gt;);</span>
  72 </pre>
  73 <div class="tip"><table border="0" summary="Tip">
  74 <tr>
  75 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../../doc/src/images/tip.png"></td>
  76 <th align="left">Tip</th>
  77 </tr>
  78 <tr><td align="left" valign="top">
  79 <p>
  80           To add two facets, <code class="computeroutput"><span class="identifier">nonfinite_num_put</span></code>
  81           and <code class="computeroutput"><span class="identifier">nonfinite_num_get</span></code>,
  82           you may have to add one at a time, using a temporary locale.
  83         </p>
  84 <p>
  85           Or you can create a new locale in one step
  86         </p>
  87 <p>
  88           <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">&lt;</span><span class="keyword">char</span><span class="special">&gt;),</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">&lt;</span><span class="keyword">char</span><span class="special">&gt;));</span></code>
  89         </p>
  90 <p>
  91           and, for example, use it to imbue an input and output stringstream.
  92         </p>
  93 </td></tr>
  94 </table></div>
  95 <div class="tip"><table border="0" summary="Tip">
  96 <tr>
  97 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../../doc/src/images/tip.png"></td>
  98 <th align="left">Tip</th>
  99 </tr>
 100 <tr><td align="left" valign="top"><p>
 101           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">&lt;</span><span class="keyword">char</span><span class="special">&gt;));</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">&lt;</span><span class="keyword">char</span><span class="special">&gt;));</span></code>
 102         </p></td></tr>
 103 </table></div>
 104 <pre class="programlisting"><span class="identifier">stringstream</span> <span class="identifier">ss</span><span class="special">;</span>
 105 <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>
 106 <span class="keyword">double</span> <span class="identifier">inf</span> <span class="special">=</span> <span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;::</span><span class="identifier">infinity</span><span class="special">();</span>
 107 <span class="identifier">ss</span> <span class="special">&lt;&lt;</span> <span class="identifier">inf</span><span class="special">;</span> <span class="comment">// Write out.</span>
 108 <span class="identifier">BOOST_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>
 109 <span class="keyword">double</span> <span class="identifier">r</span><span class="special">;</span>
 110 <span class="identifier">ss</span> <span class="special">&gt;&gt;</span> <span class="identifier">r</span><span class="special">;</span> <span class="comment">// Read back in.</span>
 111 <span class="identifier">BOOST_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>
 112
 113 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"infinity output was "</span> <span class="special">&lt;&lt;</span> <span class="identifier">ss</span><span class="special">.</span><span class="identifier">str</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
 114 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"infinity input was "</span> <span class="special">&lt;&lt;</span> <span class="identifier">r</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
 115 <span class="comment">// But the string representation of r displayed will be the native type</span>
 116 <span class="comment">// because, when it was constructed, cout had NOT been imbued</span>
 117 <span class="comment">// with the new locale containing the nonfinite_numput facet.</span>
 118 <span class="comment">// So the cout output will be "1.#INF on MS platforms</span>
 119 <span class="comment">// and may be "inf" or other string representation on other platforms.</span>
 120 </pre>
 121 <h5>
 122 <a name="math_toolkit.fp_facets.facets_intro.h2"></a>
 123         <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
 124         standard for output of infinity and NaN</a>
 125       </h5>
 126 <p>
 127         <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2011/n3242.pdf" target="_top">C++0X
 128         (final) draft standard</a> does not explicitly specify the representation
 129         (and input) of nonfinite values, leaving it implementation-defined. So without
 130         some specific action, input and output of nonfinite values is not portable.
 131       </p>
 132 <h5>
 133 <a name="math_toolkit.fp_facets.facets_intro.h3"></a>
 134         <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
 135         standard for output of infinity and NaN</a>
 136       </h5>
 137 <p>
 138         The <a href="http://www.open-std.org/JTC1/SC22/WG14/www/docs/n1256.pdf" target="_top">C99
 139         standard</a> <span class="bold"><strong>does</strong></span> specify how infinity
 140         and NaN are formatted by printf and similar output functions, and parsed
 141         by scanf and similar input functions.
 142       </p>
 143 <p>
 144         The following string representations are used:
 145       </p>
 146 <div class="table">
 147 <a name="math_toolkit.fp_facets.facets_intro.c99_representation_of_infinity_a"></a><p class="title"><b>Table&#160;2.1.&#160;C99 Representation of Infinity and NaN</b></p>
 148 <div class="table-contents"><table class="table" summary="C99 Representation of Infinity and NaN">
 149 <colgroup>
 150 <col>
 151 <col>
 152 </colgroup>
 153 <thead><tr>
 154 <th>
 155                 <p>
 156                   number
 157                 </p>
 158               </th>
 159 <th>
 160                 <p>
 161                   string
 162                 </p>
 163               </th>
 164 </tr></thead>
 165 <tbody>
 166 <tr>
 167 <td>
 168                 <p>
 169                   Positive infinity
 170                 </p>
 171               </td>
 172 <td>
 173                 <p>
 174                   "inf" or "infinity"
 175                 </p>
 176               </td>
 177 </tr>
 178 <tr>
 179 <td>
 180                 <p>
 181                   Positive NaN
 182                 </p>
 183               </td>
 184 <td>
 185                 <p>
 186                   "nan" or "nan(...)"
 187                 </p>
 188               </td>
 189 </tr>
 190 <tr>
 191 <td>
 192                 <p>
 193                   Negative infinity
 194                 </p>
 195               </td>
 196 <td>
 197                 <p>
 198                   "-inf" or "-infinity"
 199                 </p>
 200               </td>
 201 </tr>
 202 <tr>
 203 <td>
 204                 <p>
 205                   Negative NaN
 206                 </p>
 207               </td>
 208 <td>
 209                 <p>
 210                   "-nan" or "-nan(...)"
 211                 </p>
 212               </td>
 213 </tr>
 214 </tbody>
 215 </table></div>
 216 </div>
 217 <br class="table-break"><p>
 218         So following C99 provides a sensible 'standard' way of handling input and
 219         output of nonfinites in C++, and this implementation follows most of these
 220         formats.
 221       </p>
 222 <h6>
 223 <a name="math_toolkit.fp_facets.facets_intro.h4"></a>
 224         <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
 225         NaNs</a>
 226       </h6>
 227 <p>
 228         A particular type of NaN is the signaling NaN. The usual mechanism of signaling
 229         is by raising a floating-point exception. Signaling NaNs are defined by
 230         <a href="http://en.wikipedia.org/wiki/IEEE_floating-point_standard" target="_top">IEEE
 231         754-2008</a>.
 232       </p>
 233 <p>
 234         Floating-point values with layout <span class="emphasis"><em>s</em></span>111 1111 1<span class="emphasis"><em>a</em></span>xx
 235         xxxx xxxx xxxx xxxx xxxx where <span class="emphasis"><em>s</em></span> is the sign, <span class="emphasis"><em>x</em></span>
 236         is the payload, and bit <span class="emphasis"><em>a</em></span> determines the type of NaN.
 237       </p>
 238 <p>
 239         If bit <span class="emphasis"><em>a</em></span> = 1, it is a quiet NaN.
 240       </p>
 241 <p>
 242         If bit <span class="emphasis"><em>a</em></span> is zero and the payload <span class="emphasis"><em>x</em></span>
 243         is nonzero, then it is a signaling NaN.
 244       </p>
 245 <p>
 246         Although there has been theoretical interest in the ability of a signaling
 247         NaN to raise an exception, for example to prevent use of an uninitialised
 248         variable, in practice there appears to be no useful application of signaling
 249         NaNs for most current processors. <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2011/n3242.pdf" target="_top">C++0X
 250         18.3.2.2</a> still specifies a (implementation-defined) representation
 251         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
 252         if a floating-point type has a representation for signaling NaN.
 253       </p>
 254 <p>
 255         But in practice, most platforms treat signaling NaNs in the same as quiet
 256         NaNs. So, for example, they are represented by "nan" on output
 257         in <a href="http://www.open-std.org/JTC1/SC22/WG14/www/docs/n1256.pdf" target="_top">C99</a>
 258         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.
 259       </p>
 260 <div class="note"><table border="0" summary="Note">
 261 <tr>
 262 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/src/images/note.png"></td>
 263 <th align="left">Note</th>
 264 </tr>
 265 <tr><td align="left" valign="top">
 266 <p>
 267           The C99 standard does not distinguish between the quiet NaN and signaling
 268           NaN values. A quiet NaN propagates through almost every arithmetic operation
 269           without raising a floating-point exception; a signaling NaN generally raises
 270           a floating-point exception when occurring as an arithmetic operand.
 271         </p>
 272 <p>
 273           C99 specification does not define the behavior of signaling NaNs. NaNs
 274           created by IEC 60559 operations are always quiet. Therefore this implementation
 275           follows C99, and treats the signaling NaN bit as just a part of the NaN
 276           payload field. So this implementation does not distinguish between the
 277           two classes of NaN.
 278         </p>
 279 </td></tr>
 280 </table></div>
 281 <div class="note"><table border="0" summary="Note">
 282 <tr>
 283 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/src/images/note.png"></td>
 284 <th align="left">Note</th>
 285 </tr>
 286 <tr><td align="left" valign="top">
 287 <p>
 288           An implementation may give zero and non-numeric values (such as infinities
 289           and NaNs) a sign or may leave them unsigned. Wherever such values are unsigned,
 290           any requirement in the C99 Standard to retrieve the sign shall produce
 291           an unspecified sign, and any requirement to set the sign shall be ignored.
 292         </p>
 293 <p>
 294           This might apply to user-defined types, but in practice built-in floating-point
 295           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>
 296           <span class="keyword">double</span></code> have well-behaved signs.
 297         </p>
 298 </td></tr>
 299 </table></div>
 300 <p>
 301         The numbers can be of type <code class="computeroutput"><span class="keyword">float</span></code>,
 302         <code class="computeroutput"><span class="keyword">double</span></code> and <code class="computeroutput"><span class="keyword">long</span>
 303         <span class="keyword">double</span></code>. An optional + sign can be
 304         used with positive numbers (controlled by ios manipulator <code class="computeroutput"><span class="identifier">showpos</span></code>).
 305         The function <code class="computeroutput"><span class="identifier">printf</span></code> and similar
 306         C++ functions use standard formatting flags to put all lower or all upper
 307         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>
 308         and <code class="computeroutput"><span class="identifier">lowercase</span></code>).
 309       </p>
 310 <p>
 311         The function <code class="computeroutput"><span class="identifier">scanf</span></code> and similar
 312         input functions are case-insensitive.
 313       </p>
 314 <p>
 315         The dots in <code class="computeroutput"><span class="identifier">nan</span><span class="special">(...)</span></code>
 316         stand for an arbitrary string. The meaning of that string is implementation
 317         dependent. It can be used to convey extra information about the NaN, from
 318         the 'payload'. A particular value of the payload might be used to indicate
 319         a <span class="emphasis"><em>missing value</em></span>, for example.
 320       </p>
 321 <p>
 322         This library uses the string representations specified by the C99 standard.
 323       </p>
 324 <p>
 325         An example of an implementation that optionally includes the NaN payload
 326         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
 327         NaN fprintf</a>. That implementation specifies for Binary Floating Point
 328         NANs:
 329       </p>
 330 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 331 <li class="listitem">
 332             A NaN ordinal sequence is a left-parenthesis character '(', followed
 333             by a digit sequence representing an integer n, where 1 &lt;= n &lt;=
 334             INT_MAX-1, followed by a right-parenthesis character ')'.
 335           </li>
 336 <li class="listitem">
 337             The integer value, n, is determined by the fraction bits of the NaN argument
 338             value as follows:
 339           </li>
 340 <li class="listitem">
 341             For a signalling NaN value, NaN fraction bits are reversed (left to right)
 342             to produce bits (right to left) of an even integer value, 2*n. Then formatted
 343             output functions produce a (signalling) NaN ordinal sequence corresponding
 344             to the integer value n.
 345           </li>
 346 <li class="listitem">
 347             For a quiet NaN value, NaN fraction bits are reversed (left to right)
 348             to produce bits (right to left) of an odd integer value, 2*n-1. Then
 349             formatted output functions produce a (quiet) NaN ordinal sequence corresponding
 350             to the integer value n.
 351           </li>
 352 </ul></div>
 353 <div class="warning"><table border="0" summary="Warning">
 354 <tr>
 355 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Warning]" src="../../../../../../doc/src/images/warning.png"></td>
 356 <th align="left">Warning</th>
 357 </tr>
 358 <tr><td align="left" valign="top"><p>
 359           This implementation does not (yet) provide output of, or access to, the
 360           NaN payload.
 361         </p></td></tr>
 362 </table></div>
 363 </div>
 364 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 365 <td align="left"></td>
 366 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
 367       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
 368       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
 369       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
 370       Daryle Walker and Xiaogang Zhang<p>
 371         Distributed under the Boost Software License, Version 1.0. (See accompanying
 372         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>)
 373       </p>
 374 </div></td>
 375 </tr></table>
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