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| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="math_toolkit.utils.sign_functions"></a><a class="link" href="sign_functions.html" title="Sign Manipulation Functions">Sign Manipulation |
| Functions</a> |
| </h3></div></div></div> |
| <a name="math_toolkit.utils.sign_functions.synopsis"></a><h5> |
| <a name="id1323847"></a> |
| <a class="link" href="sign_functions.html#math_toolkit.utils.sign_functions.synopsis">Synopsis</a> |
| </h5> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</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">></span> |
| </pre> |
| <p> |
| </p> |
| <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"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></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"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> |
| <span class="keyword">inline</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">&</span> <span class="identifier">z</span><span class="special">);</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> |
| <span class="keyword">inline</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">&</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">y</span><span class="special">);</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> |
| <span class="keyword">inline</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">&</span> <span class="identifier">z</span><span class="special">);</span> |
| |
| <span class="special">}}</span> <span class="comment">// namespaces |
| </span></pre> |
| <a name="math_toolkit.utils.sign_functions.description"></a><h5> |
| <a name="id1324202"></a> |
| <a class="link" href="sign_functions.html#math_toolkit.utils.sign_functions.description">Description</a> |
| </h5> |
| <pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></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"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> |
| <span class="keyword">inline</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">&</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">></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"><</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"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> |
| <span class="keyword">inline</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">&</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</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"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> |
| <span class="keyword">inline</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">&</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> |
| <a name="math_toolkit.utils.sign_functions.sign_bits"></a><h6> |
| <a name="id1325339"></a> |
| <a class="link" href="sign_functions.html#math_toolkit.utils.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 then for UDT type T. |
| </p> |
| <a name="math_toolkit.utils.sign_functions.examples"></a><h6> |
| <a name="id1325375"></a> |
| <a class="link" href="sign_functions.html#math_toolkit.utils.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> |
| <a name="math_toolkit.utils.sign_functions.portability"></a><h6> |
| <a name="id1325675"></a> |
| <a class="link" href="sign_functions.html#math_toolkit.utils.sign_functions.portability">Portability</a> |
| </h6> |
| <p> |
| The library supports the following binary floating-point formats: |
| </p> |
| <div class="itemizedlist"><ul type="disc"> |
| <li> |
| IEEE 754 single precision |
| </li> |
| <li> |
| IEEE 754 double precision |
| </li> |
| <li> |
| IEEE 754 extended double precision with 15 exponent bits |
| </li> |
| <li> |
| Intel extended double precision |
| </li> |
| <li> |
| PowerPC extended double precision |
| </li> |
| <li> |
| 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 type="disc"> |
| <li> |
| Unsupported floating point formats |
| </li> |
| <li> |
| The library depends on the header boost/detail/endian.hpp |
| </li> |
| <li> |
| 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 type="disc"> |
| <li> |
| Win32 / MSVC 7.1 / 10.0 / x86 |
| </li> |
| <li> |
| Win32 / Intel C++ 7.1, 8.1, 9.1 / x86 |
| </li> |
| <li> |
| Mac OS X / GCC 3.3, 4.0 / ppc |
| </li> |
| <li> |
| Linux / Intel C++ 9.1 / x86, ia64 |
| </li> |
| <li> |
| Linux / GCC 3.3 / x86, x64, ia64, ppc, hppa, mips, m68k |
| </li> |
| <li> |
| Linux / GCC 3.4 / x64 |
| </li> |
| <li> |
| HP-UX / aCC, GCC 4.1 / ia64 |
| </li> |
| <li> |
| HP-UX / aCC / hppa |
| </li> |
| <li> |
| Tru64 / Compaq C++ 7.1 / alpha |
| </li> |
| <li> |
| VMS / HP C++ 7.1 / alpha (in IEEE floating point mode) |
| </li> |
| <li> |
| 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 © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, |
| Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and |
| Thijs van den Berg<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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