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  26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  27 <a name="math_toolkit.sign_functions"></a><a class="link" href="sign_functions.html" title="Sign Manipulation Functions">Sign Manipulation Functions</a>
  28 </h2></div></div></div>
  29 <h5>
  30 <a name="math_toolkit.sign_functions.h0"></a>
  31       <span class="phrase"><a name="math_toolkit.sign_functions.synopsis"></a></span><a class="link" href="sign_functions.html#math_toolkit.sign_functions.synopsis">Synopsis</a>
  32     </h5>
  33 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">sign</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
  34 </pre>
  35 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
  36
  37 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  38 <span class="keyword">int</span> <span class="identifier">signbit</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
  39
  40 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  41 <span class="keyword">int</span> <span class="identifier">sign</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">);</span>
  42
  43 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
  44 <span class="identifier">T</span> <span class="identifier">copysign</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">&amp;</span> <span class="identifier">y</span><span class="special">);</span>
  45
  46 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  47 <a class="link" href="result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">changesign</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">);</span>
  48
  49 <span class="special">}}</span> <span class="comment">// namespaces</span>
  50 </pre>
  51 <h5>
  52 <a name="math_toolkit.sign_functions.h1"></a>
  53       <span class="phrase"><a name="math_toolkit.sign_functions.description"></a></span><a class="link" href="sign_functions.html#math_toolkit.sign_functions.description">Description</a>
  54     </h5>
  55 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  56 <span class="keyword">int</span> <span class="identifier">signbit</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span>
  57 </pre>
  58 <p>
  59       Returns a non-zero value if the sign bit is set in variable <span class="emphasis"><em>x</em></span>,
  60       otherwise <code class="computeroutput"><span class="number">0</span></code>.
  61     </p>
  62 <div class="important"><table border="0" summary="Important">
  63 <tr>
  64 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Important]" src="../../../../../doc/src/images/important.png"></td>
  65 <th align="left">Important</th>
  66 </tr>
  67 <tr><td align="left" valign="top"><p>
  68         The return value from this function is zero or <span class="emphasis"><em>not-zero</em></span>
  69         and <span class="bold"><strong>not</strong></span> zero or one.
  70       </p></td></tr>
  71 </table></div>
  72 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  73 <span class="keyword">int</span> <span class="identifier">sign</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">);</span>
  74 </pre>
  75 <p>
  76       Returns <code class="computeroutput"><span class="number">1</span></code> if <span class="emphasis"><em>x</em></span>
  77       <code class="computeroutput"><span class="special">&gt;</span> <span class="number">0</span></code>,
  78       <code class="computeroutput"><span class="special">-</span><span class="number">1</span></code>
  79       if <span class="emphasis"><em>x</em></span> <code class="computeroutput"><span class="special">&lt;</span> <span class="number">0</span></code>, and <code class="computeroutput"><span class="number">0</span></code>
  80       if <span class="emphasis"><em>x</em></span> is zero.
  81     </p>
  82 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
  83 <a class="link" href="result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">copysign</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">&amp;</span> <span class="identifier">y</span><span class="special">);</span>
  84 </pre>
  85 <p>
  86       Sets the sign of <span class="emphasis"><em>x</em></span> to be the same as the sign of <span class="emphasis"><em>y</em></span>.
  87     </p>
  88 <p>
  89       See <a href="http://www.open-std.org/JTC1/SC22/WG14/www/docs/n1256.pdf" target="_top">C99
  90       7.12.11.1 The copysign functions</a> for more detail.
  91     </p>
  92 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  93 <span class="identifier">T</span> <span class="identifier">changesign</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">z</span><span class="special">);</span>
  94 </pre>
  95 <p>
  96       Returns a floating-point number with a binary representation where the signbit
  97       is the opposite of the sign bit in <span class="emphasis"><em>x</em></span>, and where the other
  98       bits are the same as in <span class="emphasis"><em>x</em></span>.
  99     </p>
 100 <p>
 101       This function is widely available, but not specified in any standards.
 102     </p>
 103 <p>
 104       Rationale: Not specified by TR1, but <code class="computeroutput"><span class="identifier">changesign</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span></code>
 105       is both easier to read and more efficient than
 106     </p>
 107 <pre class="programlisting"><span class="identifier">copysign</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span> <span class="identifier">signbit</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span> <span class="special">?</span> <span class="number">1.0</span> <span class="special">:</span> <span class="special">-</span><span class="number">1.0</span><span class="special">);</span>
 108 </pre>
 109 <p>
 110       For finite values, this function has the same effect as simple negation, the
 111       assignment z = -z, but for nonfinite values, <a href="http://en.wikipedia.org/wiki/Infinity#Computing" target="_top">infinities</a>
 112       and <a href="http://en.wikipedia.org/wiki/NaN" target="_top">NaNs</a>, the <code class="computeroutput"><span class="identifier">changesign</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span></code> function
 113       may be the only portable way to ensure that the sign bit is changed.
 114     </p>
 115 <h6>
 116 <a name="math_toolkit.sign_functions.h2"></a>
 117       <span class="phrase"><a name="math_toolkit.sign_functions.sign_bits"></a></span><a class="link" href="sign_functions.html#math_toolkit.sign_functions.sign_bits">Sign
 118       bits</a>
 119     </h6>
 120 <p>
 121       One of the bits in the binary representation of a floating-point number gives
 122       the sign, and the remaining bits give the absolute value. That bit is known
 123       as the sign bit. The sign bit is set = 1 for negative numbers, and is not set
 124       = 0 for positive numbers. (This is true for all binary representations of floating-point
 125       numbers that are used by modern microprocessors.)
 126     </p>
 127 <p>
 128       <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">C++
 129       TR1</a> specifies <code class="computeroutput"><span class="identifier">copysign</span></code>
 130       functions and function templates for accessing the sign bit.
 131     </p>
 132 <p>
 133       For user-defined types (UDT), the sign may be stored in some other way. They
 134       may also not provide infinity or NaNs. To use these functions with a UDT, it
 135       may be necessary to explicitly specialize them for UDT type T.
 136     </p>
 137 <h6>
 138 <a name="math_toolkit.sign_functions.h3"></a>
 139       <span class="phrase"><a name="math_toolkit.sign_functions.examples"></a></span><a class="link" href="sign_functions.html#math_toolkit.sign_functions.examples">Examples</a>
 140     </h6>
 141 <pre class="programlisting"><span class="identifier">signbit</span><span class="special">(</span><span class="number">3.5</span><span class="special">)</span> <span class="identifier">is</span> <span class="identifier">zero</span> <span class="special">(</span><span class="keyword">or</span> <span class="keyword">false</span><span class="special">)</span>
 142 <span class="identifier">signbit</span><span class="special">(-</span><span class="number">7.1</span><span class="special">)</span> <span class="identifier">is</span> <span class="number">1</span> <span class="special">(</span><span class="keyword">or</span> <span class="keyword">true</span><span class="special">)</span>
 143 <span class="identifier">copysign</span><span class="special">(</span><span class="number">4.2</span><span class="special">,</span> <span class="number">7.9</span><span class="special">)</span> <span class="identifier">is</span> <span class="number">4.2</span>
 144 <span class="identifier">copysign</span><span class="special">(</span><span class="number">3.5</span> <span class="special">-</span><span class="number">1.4</span><span class="special">)</span> <span class="identifier">is</span> <span class="special">-</span><span class="number">3.5</span>
 145 <span class="identifier">copysign</span><span class="special">(-</span><span class="number">4.2</span><span class="special">,</span> <span class="number">1.0</span><span class="special">)</span> <span class="identifier">is</span> <span class="number">4.2</span>
 146 <span class="identifier">copysign</span><span class="special">(-</span><span class="number">8.6</span><span class="special">,</span> <span class="special">-</span><span class="number">3.3</span><span class="special">)</span> <span class="identifier">is</span> <span class="special">-</span><span class="number">8.6</span>
 147 <span class="identifier">changesign</span><span class="special">(</span><span class="number">6.9</span><span class="special">)</span> <span class="identifier">is</span> <span class="special">-</span><span class="number">6.9</span>
 148 <span class="identifier">changesign</span><span class="special">(-</span><span class="number">1.8</span><span class="special">)</span> <span class="identifier">is</span> <span class="number">1.8</span>
 149 </pre>
 150 <h6>
 151 <a name="math_toolkit.sign_functions.h4"></a>
 152       <span class="phrase"><a name="math_toolkit.sign_functions.portability"></a></span><a class="link" href="sign_functions.html#math_toolkit.sign_functions.portability">Portability</a>
 153     </h6>
 154 <p>
 155       The library supports the following binary floating-point formats:
 156     </p>
 157 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 158 <li class="listitem">
 159           IEEE 754 single precision
 160         </li>
 161 <li class="listitem">
 162           IEEE 754 double precision
 163         </li>
 164 <li class="listitem">
 165           IEEE 754 extended double precision with 15 exponent bits
 166         </li>
 167 <li class="listitem">
 168           Intel extended double precision
 169         </li>
 170 <li class="listitem">
 171           PowerPC extended double precision
 172         </li>
 173 <li class="listitem">
 174           Motorola 68K extended double precision
 175         </li>
 176 </ul></div>
 177 <p>
 178       The library does not support the VAX floating-point formats. (These are available
 179       on VMS, but the default on VMS is the IEEE 754 floating-point format.)
 180     </p>
 181 <p>
 182       The main portability issues are:
 183     </p>
 184 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 185 <li class="listitem">
 186           Unsupported floating-point formats.
 187         </li>
 188 <li class="listitem">
 189           The library depends on the header <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">detail</span><span class="special">/</span><span class="identifier">endian</span><span class="special">.</span><span class="identifier">hpp</span></code>
 190           to detemine endianness.
 191         </li>
 192 <li class="listitem">
 193           Code such as <code class="computeroutput"><span class="preprocessor">#if</span> <span class="identifier">defined</span><span class="special">(</span><span class="identifier">__ia64</span><span class="special">)</span> <span class="special">||</span> <span class="identifier">defined</span><span class="special">(</span><span class="identifier">__ia64__</span><span class="special">)</span> <span class="special">||</span> <span class="identifier">defined</span><span class="special">(</span><span class="identifier">_M_IA64</span><span class="special">)</span></code> is used to determine the processor type.
 194         </li>
 195 </ul></div>
 196 <p>
 197       The library has passed all tests on the following platforms:
 198     </p>
 199 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 200 <li class="listitem">
 201           Win32 / MSVC 7.1 / 10.0 / x86 32 and 64-bit, and later Win32
 202         </li>
 203 <li class="listitem">
 204           Win32 / Intel C++ 7.1, 8.1, 9.1 / x86
 205         </li>
 206 <li class="listitem">
 207           Mac OS X / GCC 3.3, 4.0 / ppc
 208         </li>
 209 <li class="listitem">
 210           Linux / Intel C++ 9.1 / x86, ia64
 211         </li>
 212 <li class="listitem">
 213           Linux / GCC 3.3 / x86, x64, ia64, ppc, hppa, mips, m68k
 214         </li>
 215 <li class="listitem">
 216           Linux / GCC 3.4 / x64
 217         </li>
 218 <li class="listitem">
 219           HP-UX / aCC, GCC 4.1 / ia64
 220         </li>
 221 <li class="listitem">
 222           HP-UX / aCC / hppa
 223         </li>
 224 <li class="listitem">
 225           Tru64 / Compaq C++ 7.1 / alpha
 226         </li>
 227 <li class="listitem">
 228           VMS / HP C++ 7.1 / alpha (in IEEE floating-point mode)
 229         </li>
 230 <li class="listitem">
 231           VMS / HP C++ 7.2 / ia64 (in IEEE floating-point mode)
 232         </li>
 233 </ul></div>
 234 </div>
 235 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 236 <td align="left"></td>
 237 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
 238       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
 239       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
 240       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
 241       Daryle Walker and Xiaogang Zhang<p>
 242         Distributed under the Boost Software License, Version 1.0. (See accompanying
 243         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>)
 244       </p>
 245 </div></td>
 246 </tr></table>
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