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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.sign_functions"></a><a class="link" href="sign_functions.html" title="Sign Manipulation Functions">Sign Manipulation Functions</a>
</h2></div></div></div>
<h5>
<a name="math_toolkit.sign_functions.h0"></a>
      <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>
    </h5>
<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>
</pre>
<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>

<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>
<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>

<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>
<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>

<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>
<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>

<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>
<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>

<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<h5>
<a name="math_toolkit.sign_functions.h1"></a>
      <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>
    </h5>
<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>
<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>
</pre>
<p>
      Returns a non-zero value if the sign bit is set in variable <span class="emphasis"><em>x</em></span>,
      otherwise <code class="computeroutput"><span class="number">0</span></code>.
    </p>
<div class="important"><table border="0" summary="Important">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Important]" src="../../../../../doc/src/images/important.png"></td>
<th align="left">Important</th>
</tr>
<tr><td align="left" valign="top"><p>
        The return value from this function is zero or <span class="emphasis"><em>not-zero</em></span>
        and <span class="bold"><strong>not</strong></span> zero or one.
      </p></td></tr>
</table></div>
<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>
<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>
</pre>
<p>
      Returns <code class="computeroutput"><span class="number">1</span></code> if <span class="emphasis"><em>x</em></span>
      <code class="computeroutput"><span class="special">&gt;</span> <span class="number">0</span></code>,
      <code class="computeroutput"><span class="special">-</span><span class="number">1</span></code>
      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>
      if <span class="emphasis"><em>x</em></span> is zero.
    </p>
<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>
<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>
</pre>
<p>
      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>.
    </p>
<p>
      See <a href="http://www.open-std.org/JTC1/SC22/WG14/www/docs/n1256.pdf" target="_top">C99
      7.12.11.1 The copysign functions</a> for more detail.
    </p>
<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>
<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>
</pre>
<p>
      Returns a floating-point number with a binary representation where the signbit
      is the opposite of the sign bit in <span class="emphasis"><em>x</em></span>, and where the other
      bits are the same as in <span class="emphasis"><em>x</em></span>.
    </p>
<p>
      This function is widely available, but not specified in any standards.
    </p>
<p>
      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>
      is both easier to read and more efficient than
    </p>
<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>
</pre>
<p>
      For finite values, this function has the same effect as simple negation, the
      assignment z = -z, but for nonfinite values, <a href="http://en.wikipedia.org/wiki/Infinity#Computing" target="_top">infinities</a>
      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
      may be the only portable way to ensure that the sign bit is changed.
    </p>
<h6>
<a name="math_toolkit.sign_functions.h2"></a>
      <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
      bits</a>
    </h6>
<p>
      One of the bits in the binary representation of a floating-point number gives
      the sign, and the remaining bits give the absolute value. That bit is known
      as the sign bit. The sign bit is set = 1 for negative numbers, and is not set
      = 0 for positive numbers. (This is true for all binary representations of floating-point
      numbers that are used by modern microprocessors.)
    </p>
<p>
      <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">C++
      TR1</a> specifies <code class="computeroutput"><span class="identifier">copysign</span></code>
      functions and function templates for accessing the sign bit.
    </p>
<p>
      For user-defined types (UDT), the sign may be stored in some other way. They
      may also not provide infinity or NaNs. To use these functions with a UDT, it
      may be necessary to explicitly specialize them for UDT type T.
    </p>
<h6>
<a name="math_toolkit.sign_functions.h3"></a>
      <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>
    </h6>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
</pre>
<h6>
<a name="math_toolkit.sign_functions.h4"></a>
      <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>
    </h6>
<p>
      The library supports the following binary floating-point formats:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          IEEE 754 single precision
        </li>
<li class="listitem">
          IEEE 754 double precision
        </li>
<li class="listitem">
          IEEE 754 extended double precision with 15 exponent bits
        </li>
<li class="listitem">
          Intel extended double precision
        </li>
<li class="listitem">
          PowerPC extended double precision
        </li>
<li class="listitem">
          Motorola 68K extended double precision
        </li>
</ul></div>
<p>
      The library does not support the VAX floating-point formats. (These are available
      on VMS, but the default on VMS is the IEEE 754 floating-point format.)
    </p>
<p>
      The main portability issues are:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Unsupported floating-point formats.
        </li>
<li class="listitem">
          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>
          to detemine endianness.
        </li>
<li class="listitem">
          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.
        </li>
</ul></div>
<p>
      The library has passed all tests on the following platforms:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Win32 / MSVC 7.1 / 10.0 / x86 32 and 64-bit, and later Win32
        </li>
<li class="listitem">
          Win32 / Intel C++ 7.1, 8.1, 9.1 / x86
        </li>
<li class="listitem">
          Mac OS X / GCC 3.3, 4.0 / ppc
        </li>
<li class="listitem">
          Linux / Intel C++ 9.1 / x86, ia64
        </li>
<li class="listitem">
          Linux / GCC 3.3 / x86, x64, ia64, ppc, hppa, mips, m68k
        </li>
<li class="listitem">
          Linux / GCC 3.4 / x64
        </li>
<li class="listitem">
          HP-UX / aCC, GCC 4.1 / ia64
        </li>
<li class="listitem">
          HP-UX / aCC / hppa
        </li>
<li class="listitem">
          Tru64 / Compaq C++ 7.1 / alpha
        </li>
<li class="listitem">
          VMS / HP C++ 7.1 / alpha (in IEEE floating-point mode)
        </li>
<li class="listitem">
          VMS / HP C++ 7.2 / ia64 (in IEEE floating-point mode)
        </li>
</ul></div>
</div>
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<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
      Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
      R&#229;de, 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>)
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