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<a name="boost_integer.extended_euclidean"></a><a class="link" href="extended_euclidean.html" title="Extended Euclidean Algorithm">Extended Euclidean Algorithm</a>
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<a name="boost_integer.extended_euclidean.introduction"></a><a class="link" href="extended_euclidean.html#boost_integer.extended_euclidean.introduction" title="Introduction">Introduction</a>
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<p>
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The extended Euclidean algorithm solves the integer relation <span class="emphasis"><em>mx
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+ ny</em></span> = gcd(<span class="emphasis"><em>m</em></span>, <span class="emphasis"><em>n</em></span>) for
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<span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>.
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</h3></div></div></div>
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<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">integer</span><span class="special">/</span><span class="identifier">extended_euclidean</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
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<span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">integer</span> <span class="special">{</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">Z</span><span class="special">></span>
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<span class="keyword">struct</span> <span class="identifier">euclidean_result_t</span> <span class="special">{</span>
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<span class="identifier">Z</span> <span class="identifier">gcd</span><span class="special">;</span>
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<span class="identifier">Z</span> <span class="identifier">x</span><span class="special">;</span>
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<span class="identifier">Z</span> <span class="identifier">y</span><span class="special">;</span>
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<span class="special">};</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">Z</span><span class="special">></span>
|
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<span class="identifier">euclidean_result_t</span><span class="special"><</span><span class="identifier">Z</span><span class="special">></span> <span class="identifier">extended_euclidean</span><span class="special">(</span><span class="identifier">Z</span> <span class="identifier">m</span><span class="special">,</span> <span class="identifier">Z</span> <span class="identifier">n</span><span class="special">);</span>
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<span class="special">}}</span>
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</pre>
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</div>
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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="boost_integer.extended_euclidean.usage"></a><a class="link" href="extended_euclidean.html#boost_integer.extended_euclidean.usage" title="Usage">Usage</a>
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</h3></div></div></div>
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<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">m</span> <span class="special">=</span> <span class="number">12</span><span class="special">;</span>
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<span class="keyword">int</span> <span class="identifier">n</span> <span class="special">=</span> <span class="number">15</span><span class="special">;</span>
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<span class="keyword">auto</span> <span class="identifier">res</span> <span class="special">=</span> <span class="identifier">extended_euclidean</span><span class="special">(</span><span class="identifier">m</span><span class="special">,</span> <span class="identifier">n</span><span class="special">);</span>
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<span class="keyword">int</span> <span class="identifier">gcd</span> <span class="special">=</span> <span class="identifier">res</span><span class="special">.</span><span class="identifier">gcd</span><span class="special">;</span>
|
||||
<span class="keyword">int</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">res</span><span class="special">.</span><span class="identifier">x</span><span class="special">;</span>
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<span class="keyword">int</span> <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">res</span><span class="special">.</span><span class="identifier">y</span><span class="special">;</span>
|
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<span class="comment">// mx + ny = gcd(m,n) should now hold</span>
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</pre>
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<p>
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Unlike most of the library, the extended Euclidean algorithm requires C++11
|
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features.
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</p>
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</div>
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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="boost_integer.extended_euclidean.references"></a><a class="link" href="extended_euclidean.html#boost_integer.extended_euclidean.references" title="References">References</a>
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</h3></div></div></div>
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<p>
|
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Wagstaff, Samuel S., <span class="emphasis"><em>The Joy of Factoring</em></span>, Vol. 68.
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American Mathematical Soc., 2013.
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</p>
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</div>
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2001-2009 Beman
|
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Dawes, Daryle Walker, Gennaro Prota, John Maddock<p>
|
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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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<div class="toc"><dl class="toc">
|
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<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.introduction">Introduction</a></span></dt>
|
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<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.synopsis">Synopsis</a></span></dt>
|
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<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_function_object">GCD Function
|
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Object</a></span></dt>
|
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<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.lcm_function_object">LCM Function
|
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Object</a></span></dt>
|
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<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.run_time">Run-time GCD & LCM
|
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Determination</a></span></dt>
|
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<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.compile_time">Compile time GCD
|
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and LCM determination</a></span></dt>
|
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<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_header">Header <boost/integer/common_factor.hpp></a></span></dt>
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|
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|
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|
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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="boost_integer.gcd_lcm.introduction"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.introduction" title="Introduction">Introduction</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The class and function templates in <boost/math/common_factor.hpp>
|
||||
provide run-time and compile-time evaluation of the greatest common divisor
|
||||
(GCD) or least common multiple (LCM) of two integers. These facilities are
|
||||
useful for many numeric-oriented generic programming problems.
|
||||
</p>
|
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</div>
|
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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="boost_integer.gcd_lcm.synopsis"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.synopsis" title="Synopsis">Synopsis</a>
|
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</h3></div></div></div>
|
||||
<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">integer</span>
|
||||
<span class="special">{</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
||||
<span class="keyword">class</span> <span class="identifier">gcd_evaluator</span><span class="special">;</span>
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
||||
<span class="keyword">class</span> <span class="identifier">lcm_evaluator</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
||||
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">gcd</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">);</span>
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
||||
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">lcm</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">);</span>
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span><span class="special">,</span> <span class="keyword">typename</span><span class="special">...</span> <span class="identifier">Args</span> <span class="special">></span>
|
||||
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">gcd</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">Args</span> <span class="keyword">const</span><span class="special">&...</span> <span class="special">);</span>
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span><span class="special">,</span> <span class="keyword">typename</span><span class="special">...</span> <span class="identifier">Args</span> <span class="special">></span>
|
||||
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">lcm</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">Args</span> <span class="keyword">const</span><span class="special">&...</span> <span class="special">);</span>
|
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|
||||
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">typename</span> <span class="identifier">I</span><span class="special">></span>
|
||||
<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special"><</span><span class="identifier">I</span><span class="special">>::</span><span class="identifier">value_type</span><span class="special">,</span> <span class="identifier">I</span><span class="special">></span>
|
||||
<span class="identifier">gcd_range</span><span class="special">(</span><span class="identifier">I</span> <span class="identifier">first</span><span class="special">,</span> <span class="identifier">I</span> <span class="identifier">last</span><span class="special">);</span>
|
||||
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">typename</span> <span class="identifier">I</span><span class="special">></span>
|
||||
<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special"><</span><span class="identifier">I</span><span class="special">>::</span><span class="identifier">value_type</span><span class="special">,</span> <span class="identifier">I</span><span class="special">></span>
|
||||
<span class="identifier">lcm_range</span><span class="special">(</span><span class="identifier">I</span> <span class="identifier">first</span><span class="special">,</span> <span class="identifier">I</span> <span class="identifier">last</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">typedef</span> <span class="emphasis"><em>see-below</em></span> <span class="identifier">static_gcd_type</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="identifier">static_gcd_type</span> <span class="identifier">Value1</span><span class="special">,</span> <span class="identifier">static_gcd_type</span> <span class="identifier">Value2</span> <span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">static_gcd</span><span class="special">;</span>
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="identifier">static_gcd_type</span> <span class="identifier">Value1</span><span class="special">,</span> <span class="identifier">static_gcd_type</span> <span class="identifier">Value2</span> <span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">static_lcm</span><span class="special">;</span>
|
||||
|
||||
<span class="special">}</span>
|
||||
<span class="special">}</span>
|
||||
</pre>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.gcd_lcm.gcd_function_object"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_function_object" title="GCD Function Object">GCD Function
|
||||
Object</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/integer/common_factor_rt.hpp" target="_top"><boost/integer/common_factor_rt.hpp></a>
|
||||
</p>
|
||||
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
||||
<span class="keyword">class</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">gcd_evaluator</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">public</span><span class="special">:</span>
|
||||
<span class="comment">// Types</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">result_type</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">first_argument_type</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">second_argument_type</span><span class="special">;</span>
|
||||
|
||||
<span class="comment">// Function object interface</span>
|
||||
<span class="keyword">constexpr</span> <span class="identifier">result_type</span> <span class="keyword">operator</span> <span class="special">()(</span>
|
||||
<span class="identifier">first_argument_type</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span>
|
||||
<span class="identifier">second_argument_type</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
||||
</pre>
|
||||
<p>
|
||||
The boost::integer::gcd_evaluator class template defines a function object
|
||||
class to return the greatest common divisor of two integers. The template
|
||||
is parameterized by a single type, called IntegerType here. This type should
|
||||
be a numeric type that represents integers. The result of the function object
|
||||
is always nonnegative, even if either of the operator arguments is negative.
|
||||
</p>
|
||||
<p>
|
||||
This function object class template is used in the corresponding version
|
||||
of the GCD function template. If a numeric type wants to customize evaluations
|
||||
of its greatest common divisors, then the type should specialize on the gcd_evaluator
|
||||
class template.
|
||||
</p>
|
||||
<p>
|
||||
Note that these function objects are <code class="computeroutput"><span class="keyword">constexpr</span></code>
|
||||
in C++14 and later only. They are also declared <code class="computeroutput"><span class="keyword">noexcept</span></code>
|
||||
when appropriate.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.gcd_lcm.lcm_function_object"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.lcm_function_object" title="LCM Function Object">LCM Function
|
||||
Object</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/integer/common_factor_rt.hpp" target="_top"><boost/integer/common_factor_rt.hpp></a>
|
||||
</p>
|
||||
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
||||
<span class="keyword">class</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">lcm_evaluator</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">public</span><span class="special">:</span>
|
||||
<span class="comment">// Types</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">result_type</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">first_argument_type</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">IntegerType</span> <span class="identifier">second_argument_type</span><span class="special">;</span>
|
||||
|
||||
<span class="comment">// Function object interface</span>
|
||||
<span class="keyword">constexpr</span> <span class="identifier">result_type</span> <span class="keyword">operator</span> <span class="special">()(</span>
|
||||
<span class="identifier">first_argument_type</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span>
|
||||
<span class="identifier">second_argument_type</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
||||
</pre>
|
||||
<p>
|
||||
The boost::integer::lcm_evaluator class template defines a function object
|
||||
class to return the least common multiple of two integers. The template is
|
||||
parameterized by a single type, called IntegerType here. This type should
|
||||
be a numeric type that represents integers. The result of the function object
|
||||
is always nonnegative, even if either of the operator arguments is negative.
|
||||
If the least common multiple is beyond the range of the integer type, the
|
||||
results are undefined.
|
||||
</p>
|
||||
<p>
|
||||
This function object class template is used in the corresponding version
|
||||
of the LCM function template. If a numeric type wants to customize evaluations
|
||||
of its least common multiples, then the type should specialize on the lcm_evaluator
|
||||
class template.
|
||||
</p>
|
||||
<p>
|
||||
Note that these function objects are constexpr in C++14 and later only. They
|
||||
are also declared <code class="computeroutput"><span class="keyword">noexcept</span></code> when
|
||||
appropriate.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.gcd_lcm.run_time"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.run_time" title="Run-time GCD & LCM Determination">Run-time GCD & LCM
|
||||
Determination</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/integer/common_factor_rt.hpp" target="_top"><boost/integer/common_factor_rt.hpp></a>
|
||||
</p>
|
||||
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
||||
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">gcd</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">></span>
|
||||
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">lcm</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span> <span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span><span class="special">,</span> <span class="keyword">typename</span><span class="special">...</span> <span class="identifier">Args</span> <span class="special">></span>
|
||||
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">gcd</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">Args</span> <span class="keyword">const</span><span class="special">&...</span> <span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span><span class="special">,</span> <span class="keyword">typename</span><span class="special">...</span> <span class="identifier">Args</span> <span class="special">></span>
|
||||
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">lcm</span><span class="special">(</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">Args</span> <span class="keyword">const</span><span class="special">&...</span> <span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">typename</span> <span class="identifier">I</span><span class="special">></span>
|
||||
<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special"><</span><span class="identifier">I</span><span class="special">>::</span><span class="identifier">value_type</span><span class="special">,</span> <span class="identifier">I</span><span class="special">></span>
|
||||
<span class="identifier">gcd_range</span><span class="special">(</span><span class="identifier">I</span> <span class="identifier">first</span><span class="special">,</span> <span class="identifier">I</span> <span class="identifier">last</span><span class="special">);</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">typename</span> <span class="identifier">I</span><span class="special">></span>
|
||||
<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special"><</span><span class="identifier">I</span><span class="special">>::</span><span class="identifier">value_type</span><span class="special">,</span> <span class="identifier">I</span><span class="special">></span>
|
||||
<span class="identifier">lcm_range</span><span class="special">(</span><span class="identifier">I</span> <span class="identifier">first</span><span class="special">,</span> <span class="identifier">I</span> <span class="identifier">last</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
The boost::integer::gcd function template returns the greatest common (nonnegative)
|
||||
divisor of the two integers passed to it. <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">gcd_range</span></code>
|
||||
is the iteration of the above gcd algorithm over a range, returning the greatest
|
||||
common divisor of all the elements. The algorithm terminates when the gcd
|
||||
reaches unity or the end of the range. Thus it also returns the iterator
|
||||
after the last element inspected because this may not be equal to the end
|
||||
of the range. The variadic version of <code class="computeroutput"><span class="identifier">gcd</span></code>
|
||||
behaves similarly but does not indicate which input value caused the gcd
|
||||
to reach unity.
|
||||
</p>
|
||||
<p>
|
||||
The boost::integer::lcm function template returns the least common (nonnegative)
|
||||
multiple of the two integers passed to it. As with gcd, there are range and
|
||||
variadic versions of the function for more than 2 arguments.
|
||||
</p>
|
||||
<p>
|
||||
Note that these functions are constexpr in C++14 and later only. They are
|
||||
also declared <code class="computeroutput"><span class="keyword">noexcept</span></code> when
|
||||
appropriate.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.gcd_lcm.compile_time"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.compile_time" title="Compile time GCD and LCM determination">Compile time GCD
|
||||
and LCM determination</a>
|
||||
</h3></div></div></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>
|
||||
These functions are deprecated in favor of constexpr <code class="computeroutput"><span class="identifier">gcd</span></code>
|
||||
and <code class="computeroutput"><span class="identifier">lcm</span></code> on C++14 capable
|
||||
compilers.
|
||||
</p></td></tr>
|
||||
</table></div>
|
||||
<p>
|
||||
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/integer/common_factor_ct.hpp" target="_top"><boost/integer/common_factor_ct.hpp></a>
|
||||
</p>
|
||||
<pre class="programlisting"><span class="keyword">typedef</span> <span class="emphasis"><em>unspecified</em></span> <span class="identifier">static_gcd_type</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="identifier">static_gcd_type</span> <span class="identifier">Value1</span><span class="special">,</span> <span class="identifier">static_gcd_type</span> <span class="identifier">Value2</span> <span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">static_gcd</span> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special"><</span><span class="identifier">static_gcd_type</span><span class="special">,</span> <span class="identifier">implementation_defined</span><span class="special">></span>
|
||||
<span class="special">{</span>
|
||||
<span class="special">};</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="identifier">static_gcd_type</span> <span class="identifier">Value1</span><span class="special">,</span> <span class="identifier">static_gcd_type</span> <span class="identifier">Value2</span> <span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">static_lcm</span> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special"><</span><span class="identifier">static_gcd_type</span><span class="special">,</span> <span class="identifier">implementation_defined</span><span class="special">></span>
|
||||
<span class="special">{</span>
|
||||
<span class="special">};</span>
|
||||
</pre>
|
||||
<p>
|
||||
The type <code class="computeroutput"><span class="identifier">static_gcd_type</span></code>
|
||||
is the widest unsigned-integer-type that is supported for use in integral-constant-expressions
|
||||
by the compiler. Usually this the same type as <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span></code>,
|
||||
but may fall back to being <code class="computeroutput"><span class="keyword">unsigned</span>
|
||||
<span class="keyword">long</span></code> for some older compilers.
|
||||
</p>
|
||||
<p>
|
||||
The boost::integer::static_gcd and boost::integer::static_lcm class templates
|
||||
take two value-based template parameters of the <span class="emphasis"><em>static_gcd_type</em></span>
|
||||
type and inherit from the type <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span></code>. Inherited from the base class,
|
||||
they have a member <span class="emphasis"><em>value</em></span> that is the greatest common
|
||||
factor or least common multiple, respectively, of the template arguments.
|
||||
A compile-time error will occur if the least common multiple is beyond the
|
||||
range of <code class="computeroutput"><span class="identifier">static_gcd_type</span></code>.
|
||||
</p>
|
||||
<h4>
|
||||
<a name="boost_integer.gcd_lcm.compile_time.h0"></a>
|
||||
<span class="phrase"><a name="boost_integer.gcd_lcm.compile_time.example"></a></span><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.compile_time.example">Example</a>
|
||||
</h4>
|
||||
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">integer</span><span class="special">/</span><span class="identifier">common_factor</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
|
||||
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">algorithm</span><span class="special">></span>
|
||||
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iterator</span><span class="special">></span>
|
||||
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span>
|
||||
|
||||
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">;</span>
|
||||
<span class="keyword">using</span> <span class="identifier">std</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">"The GCD and LCM of 6 and 15 are "</span>
|
||||
<span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">gcd</span><span class="special">(</span><span class="number">6</span><span class="special">,</span> <span class="number">15</span><span class="special">)</span> <span class="special"><<</span> <span class="string">" and "</span>
|
||||
<span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">lcm</span><span class="special">(</span><span class="number">6</span><span class="special">,</span> <span class="number">15</span><span class="special">)</span> <span class="special"><<</span> <span class="string">", respectively."</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">"The GCD and LCM of 8 and 9 are "</span>
|
||||
<span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">static_gcd</span><span class="special"><</span><span class="number">8</span><span class="special">,</span> <span class="number">9</span><span class="special">>::</span><span class="identifier">value</span>
|
||||
<span class="special"><<</span> <span class="string">" and "</span>
|
||||
<span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">static_lcm</span><span class="special"><</span><span class="number">8</span><span class="special">,</span> <span class="number">9</span><span class="special">>::</span><span class="identifier">value</span>
|
||||
<span class="special"><<</span> <span class="string">", respectively."</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">int</span> <span class="identifier">a</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">4</span><span class="special">,</span> <span class="number">5</span><span class="special">,</span> <span class="number">6</span> <span class="special">},</span> <span class="identifier">b</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">7</span><span class="special">,</span> <span class="number">8</span><span class="special">,</span> <span class="number">9</span> <span class="special">},</span> <span class="identifier">c</span><span class="special">[</span><span class="number">3</span><span class="special">];</span>
|
||||
<span class="identifier">std</span><span class="special">::</span><span class="identifier">transform</span><span class="special">(</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">a</span> <span class="special">+</span> <span class="number">3</span><span class="special">,</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">c</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">integer</span><span class="special">::</span><span class="identifier">gcd_evaluator</span><span class="special"><</span><span class="keyword">int</span><span class="special">>()</span> <span class="special">);</span>
|
||||
<span class="identifier">std</span><span class="special">::</span><span class="identifier">copy</span><span class="special">(</span> <span class="identifier">c</span><span class="special">,</span> <span class="identifier">c</span> <span class="special">+</span> <span class="number">3</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream_iterator</span><span class="special"><</span><span class="keyword">int</span><span class="special">>(</span><span class="identifier">cout</span><span class="special">,</span> <span class="string">" "</span><span class="special">)</span> <span class="special">);</span>
|
||||
<span class="special">}</span>
|
||||
</pre>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.gcd_lcm.gcd_header"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_header" title="Header <boost/integer/common_factor.hpp>">Header <boost/integer/common_factor.hpp></a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
This header simply includes the headers <a href="../../../../../boost/integer/common_factor_ct.hpp" target="_top"><boost/integer/common_factor_ct.hpp></a>
|
||||
and <a href="../../../../../boost/integer/common_factor_rt.hpp" target="_top"><boost/integer/common_factor_rt.hpp></a>.
|
||||
</p>
|
||||
<p>
|
||||
Note this is a legacy header: it used to contain the actual implementation,
|
||||
but the compile-time and run-time facilities were moved to separate headers
|
||||
(since they were independent of each other).
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.gcd_lcm.demo"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.demo" title="Demonstration Program">Demonstration Program</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The program <a href="../../../../../libs/integer/test/common_factor_test.cpp" target="_top">common_factor_test.cpp</a>
|
||||
is a demonstration of the results from instantiating various examples of
|
||||
the run-time GCD and LCM function templates and the compile-time GCD and
|
||||
LCM class templates. (The run-time GCD and LCM class templates are tested
|
||||
indirectly through the run-time function templates.)
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.gcd_lcm.rationale"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.rationale" title="Rationale">Rationale</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The greatest common divisor and least common multiple functions are greatly
|
||||
used in some numeric contexts, including some of the other Boost libraries.
|
||||
Centralizing these functions to one header improves code factoring and eases
|
||||
maintenance.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.gcd_lcm.gcd_history"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_history" title="History">History</a>
|
||||
</h3></div></div></div>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
||||
<li class="listitem">
|
||||
24th April 2017 Moved to Jeremy Murphy's improved algorithms, added constexpr
|
||||
and noexcept support, added compiler intrinsic support, added variadic
|
||||
and range based versions of the algorithms.
|
||||
</li>
|
||||
<li class="listitem">
|
||||
13 May 2013 Moved into main Boost.Math Quickbook documentation.
|
||||
</li>
|
||||
<li class="listitem">
|
||||
17 Dec 2005: Converted documentation to Quickbook Format.
|
||||
</li>
|
||||
<li class="listitem">
|
||||
2 Jul 2002: Compile-time and run-time items separated to new headers.
|
||||
</li>
|
||||
<li class="listitem">
|
||||
7 Nov 2001: Initial version
|
||||
</li>
|
||||
</ul></div>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.gcd_lcm.gcd_credits"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_credits" title="Credits">Credits</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The author of the Boost compilation of GCD and LCM computations is Daryle
|
||||
Walker. The code was prompted by existing code hiding in the implementations
|
||||
of Paul Moore's rational library and Steve Cleary's pool library. The code
|
||||
had updates by Helmut Zeisel.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
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|
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<td align="right"><div class="copyright-footer">Copyright © 2001-2009 Beman
|
||||
Dawes, Daryle Walker, Gennaro Prota, John Maddock<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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|
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Moved <code class="computeroutput"><span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">cstdint</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> into <a href="../../../../../libs/config/index.html" target="_top">Boost.Config</a>.
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<span class="phrase"><a name="boost_integer.history.1_42_0"></a></span><a class="link" href="history.html#boost_integer.history.1_42_0">1.42.0</a>
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Reverted Trunk to release branch state (i.e. a "known good state").
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<li class="listitem">
|
||||
Fixed issues: <a href="https://svn.boost.org/trac/boost/ticket/653" target="_top">653</a>,
|
||||
<a href="https://svn.boost.org/trac/boost/ticket/3084" target="_top">3084</a>,
|
||||
<a href="https://svn.boost.org/trac/boost/ticket/3177" target="_top">3177</a>,
|
||||
<a href="https://svn.boost.org/trac/boost/ticket/3180" target="_top">3180</a>,
|
||||
<a href="https://svn.boost.org/trac/boost/ticket/3548" target="_top">3568</a>,
|
||||
<a href="https://svn.boost.org/trac/boost/ticket/3657" target="_top">3657</a>,
|
||||
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|
||||
</li>
|
||||
<li class="listitem">
|
||||
Added long long support to <code class="literal">boost::static_log2</code>, <code class="literal">boost::static_signed_min</code>,
|
||||
<code class="literal">boost::static_signed_max</code>, <code class="literal">boost::static_unsigned_min</code><code class="literal">boost::static_unsigned_max</code>,
|
||||
when available.
|
||||
</li>
|
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<li class="listitem">
|
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The argument type and the result type of <code class="literal">boost::static_signed_min</code>
|
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etc are now typedef'd. Formerly, they were hardcoded as <code class="literal">unsigned
|
||||
long</code> and <code class="literal">int</code> respectively. Please, use the
|
||||
provided typedefs in new code (and update old code as soon as possible).
|
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</li>
|
||||
</ul></div>
|
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<h5>
|
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<a name="boost_integer.history.h2"></a>
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<span class="phrase"><a name="boost_integer.history.1_32_0"></a></span><a class="link" href="history.html#boost_integer.history.1_32_0">1.32.0</a>
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</h5>
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
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The argument type and the result type of <code class="literal">boost::static_log2</code>
|
||||
are now typedef'd. Formerly, they were hardcoded as <code class="literal">unsigned long</code>
|
||||
and <code class="literal">int</code> respectively. Please, use the provided typedefs
|
||||
in new code (and update old code as soon as possible).
|
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</li></ul></div>
|
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright © 2001-2009 Beman
|
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Dawes, Daryle Walker, Gennaro Prota, John Maddock<p>
|
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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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|
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<p>
|
||||
The <a href="../../../../../boost/integer.hpp" target="_top"><boost/integer.hpp></a>
|
||||
type selection templates allow integer types to be selected based on desired
|
||||
characteristics such as number of bits or maximum value. This facility is particularly
|
||||
useful for solving generic programming problems.
|
||||
</p>
|
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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="boost_integer.integer.synopsis"></a><a class="link" href="integer.html#boost_integer.integer.synopsis" title="Synopsis">Synopsis</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span>
|
||||
<span class="special">{</span>
|
||||
<span class="comment">// fast integers from least integers</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">LeastInt</span><span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">int_fast_t</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">typedef</span> <span class="emphasis"><em>implementation-defined-type</em></span> <span class="identifier">type</span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
||||
|
||||
<span class="comment">// signed</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">int</span> <span class="identifier">Bits</span><span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">int_t</span>
|
||||
<span class="special">{</span>
|
||||
<span class="comment">/* Member exact may or may not be defined depending upon Bits */</span>
|
||||
<span class="keyword">typedef</span> <span class="emphasis"><em>implementation-defined-type</em></span> <span class="identifier">exact</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="emphasis"><em>implementation-defined-type</em></span> <span class="identifier">least</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">int_fast_t</span><span class="special"><</span><span class="identifier">least</span><span class="special">>::</span><span class="identifier">fast</span> <span class="identifier">fast</span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
||||
|
||||
<span class="comment">// unsigned</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">int</span> <span class="identifier">Bits</span><span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">uint_t</span>
|
||||
<span class="special">{</span>
|
||||
<span class="comment">/* Member exact may or may not be defined depending upon Bits */</span>
|
||||
<span class="keyword">typedef</span> <span class="emphasis"><em>implementation-defined-type</em></span> <span class="identifier">exact</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="emphasis"><em>implementation-defined-type</em></span> <span class="identifier">least</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">int_fast_t</span><span class="special"><</span><span class="identifier">least</span><span class="special">>::</span><span class="identifier">fast</span> <span class="identifier">fast</span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
||||
|
||||
<span class="comment">// signed</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">MaxValue</span><span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">int_max_value_t</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">typedef</span> <span class="emphasis"><em>implementation-defined-type</em></span> <span class="identifier">least</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">int_fast_t</span><span class="special"><</span><span class="identifier">least</span><span class="special">>::</span><span class="identifier">fast</span> <span class="identifier">fast</span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">MinValue</span><span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">int_min_value_t</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">typedef</span> <span class="emphasis"><em>implementation-defined-type</em></span> <span class="identifier">least</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">int_fast_t</span><span class="special"><</span><span class="identifier">least</span><span class="special">>::</span><span class="identifier">fast</span> <span class="identifier">fast</span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
||||
|
||||
<span class="comment">// unsigned</span>
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">Value</span><span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">uint_value_t</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">typedef</span> <span class="emphasis"><em>implementation-defined-type</em></span> <span class="identifier">least</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">int_fast_t</span><span class="special"><</span><span class="identifier">least</span><span class="special">>::</span><span class="identifier">fast</span> <span class="identifier">fast</span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
||||
<span class="special">}</span> <span class="comment">// namespace boost</span>
|
||||
</pre>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.integer.easiest"></a><a class="link" href="integer.html#boost_integer.integer.easiest" title="Easiest-to-Manipulate Types">Easiest-to-Manipulate
|
||||
Types</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The <code class="literal">int_fast_t</code> class template maps its input type to the
|
||||
next-largest type that the processor can manipulate the easiest, or to itself
|
||||
if the input type is already an easy-to-manipulate type. For instance, processing
|
||||
a bunch of <code class="literal">char</code> objects may go faster if they were converted
|
||||
to <code class="literal">int</code> objects before processing. The input type, passed
|
||||
as the only template parameter, must be a built-in integral type, except
|
||||
<code class="literal">bool</code>. Unsigned integral types can be used, as well as
|
||||
signed integral types. The output type is given as the nested type <code class="literal">fast</code>.
|
||||
</p>
|
||||
<p>
|
||||
<span class="bold"><strong>Implementation Notes:</strong></span> By default, the output
|
||||
type is identical to the input type. Eventually, this code's implementation
|
||||
should be customized for each platform to give accurate mappings between
|
||||
the built-in types and the easiest-to-manipulate built-in types. Also, there
|
||||
is no guarantee that the output type actually is easier to manipulate than
|
||||
the input type.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.integer.sized"></a><a class="link" href="integer.html#boost_integer.integer.sized" title="Sized Types">Sized Types</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The <code class="literal">int_t</code>, <code class="literal">uint_t</code>, <code class="literal">int_max_value_t</code>,
|
||||
<code class="literal">int_min_value_t</code>, and <code class="literal">uint_value_t</code> class
|
||||
templates find the most appropiate built-in integral type for the given template
|
||||
parameter. This type is given by the nested type <code class="literal">least</code>.
|
||||
The easiest-to-manipulate version of that type is given by the nested type
|
||||
<code class="literal">fast</code>. The following table describes each template's criteria.
|
||||
</p>
|
||||
<div class="table">
|
||||
<a name="boost_integer.integer.sized.criteria_for_the_sized_type_class_templates"></a><p class="title"><b>Table 1. Criteria for the Sized Type Class Templates</b></p>
|
||||
<div class="table-contents"><table class="table" summary="Criteria for the Sized Type Class Templates">
|
||||
<colgroup>
|
||||
<col>
|
||||
<col>
|
||||
</colgroup>
|
||||
<thead><tr>
|
||||
<th>
|
||||
<p>
|
||||
Class Template
|
||||
</p>
|
||||
</th>
|
||||
<th>
|
||||
<p>
|
||||
Template Parameter Mapping
|
||||
</p>
|
||||
</th>
|
||||
</tr></thead>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">boost::int_t<N>::least</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
The smallest, built-in, signed integral type with at least <span class="emphasis"><em>N</em></span>
|
||||
bits, including the sign bit. The parameter should be a positive
|
||||
number. A compile-time error results if the parameter is larger
|
||||
than the number of bits in the largest integer type.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">boost::int_t<N>::fast</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
The easiest-to-manipulate, built-in, signed integral type with
|
||||
at least <span class="emphasis"><em>N</em></span> bits, including the sign bit. The
|
||||
parameter should be a positive number. A compile-time error results
|
||||
if the parameter is larger than the number of bits in the largest
|
||||
integer type.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">boost::int_t<N>::exact</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
A built-in, signed integral type with exactly <span class="emphasis"><em>N</em></span>
|
||||
bits, including the sign bit. The parameter should be a positive
|
||||
number. Note that the member <span class="emphasis"><em>exact</em></span> is defined
|
||||
<span class="bold"><strong>only</strong></span> if there exists a type with
|
||||
exactly <span class="emphasis"><em>N</em></span> bits.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">boost::uint_t<N>::least</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
The smallest, built-in, unsigned integral type with at least <span class="emphasis"><em>N</em></span>
|
||||
bits. The parameter should be a positive number. A compile-time
|
||||
error results if the parameter is larger than the number of bits
|
||||
in the largest integer type.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">boost::uint_t<N>::fast</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
The easiest-to-manipulate, built-in, unsigned integral type with
|
||||
at least <span class="emphasis"><em>N</em></span> bits. The parameter should be a
|
||||
positive number. A compile-time error results if the parameter
|
||||
is larger than the number of bits in the largest integer type.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">boost::uint_t<N>::exact</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
A built-in, unsigned integral type with exactly <span class="emphasis"><em>N</em></span>
|
||||
bits. The parameter should be a positive number. A compile-time
|
||||
error results if the parameter is larger than the number of bits
|
||||
in the largest integer type. Note that the member <span class="emphasis"><em>exact</em></span>
|
||||
is defined <span class="bold"><strong>only</strong></span> if there exists
|
||||
a type with exactly N bits.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">boost::int_max_value_t<V>::last</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
The smallest, built-in, signed integral type that can hold all
|
||||
the values in the inclusive range <span class="emphasis"><em>0 - V</em></span>. The
|
||||
parameter should be a positive number.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">boost::int_max_value_t<V>::fast</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
The easiest-to-manipulate, built-in, signed integral type that
|
||||
can hold all the values in the inclusive range <span class="emphasis"><em>0 - V</em></span>.
|
||||
The parameter should be a positive number.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">boost::int_min_value_t<V>::least</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
The smallest, built-in, signed integral type that can hold all
|
||||
the values in the inclusive range <span class="emphasis"><em>V - 0</em></span>. The
|
||||
parameter should be a negative number.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">boost::int_min_value_t<V>::fast</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
The easiest-to-manipulate, built-in, signed integral type that
|
||||
can hold all the values in the inclusive range <span class="emphasis"><em>V - 0</em></span>.
|
||||
The parameter should be a negative number.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">boost::uint_value_t<V>::least</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
The smallest, built-in, unsigned integral type that can hold all
|
||||
positive values up to and including <span class="emphasis"><em>V</em></span>. The
|
||||
parameter should be a positive number.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">boost::uint_value_t<V>::fast</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
The easiest-to-manipulate, built-in, unsigned integral type that
|
||||
can hold all positive values up to and including <span class="emphasis"><em>V</em></span>.
|
||||
The parameter should be a positive number.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
</div>
|
||||
<br class="table-break">
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.integer.example"></a><a class="link" href="integer.html#boost_integer.integer.example" title="Example">Example</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">integer</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
|
||||
|
||||
<span class="comment">//...</span>
|
||||
|
||||
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
|
||||
<span class="special">{</span>
|
||||
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">int_t</span><span class="special"><</span><span class="number">24</span><span class="special">>::</span><span class="identifier">least</span> <span class="identifier">my_var</span><span class="special">;</span> <span class="comment">// my_var has at least 24-bits</span>
|
||||
<span class="comment">//...</span>
|
||||
<span class="comment">// This one is guaranteed not to be truncated:</span>
|
||||
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">int_max_value_t</span><span class="special"><</span><span class="number">1000</span><span class="special">>::</span><span class="identifier">least</span> <span class="identifier">my1000</span> <span class="special">=</span> <span class="number">1000</span><span class="special">;</span>
|
||||
<span class="comment">//...</span>
|
||||
<span class="comment">// This one is guaranteed not to be truncated, and as fast</span>
|
||||
<span class="comment">// to manipulate as possible, its size may be greater than</span>
|
||||
<span class="comment">// that of my1000:</span>
|
||||
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">int_max_value_t</span><span class="special"><</span><span class="number">1000</span><span class="special">>::</span><span class="identifier">fast</span> <span class="identifier">my_fast1000</span> <span class="special">=</span> <span class="number">1000</span><span class="special">;</span>
|
||||
<span class="special">}</span>
|
||||
</pre>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.integer.demonstration_program"></a><a class="link" href="integer.html#boost_integer.integer.demonstration_program" title="Demonstration Program">Demonstration
|
||||
Program</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The program <a href="../../../test/integer_test.cpp" target="_top">integer_test.cpp</a>
|
||||
is a simplistic demonstration of the results from instantiating various examples
|
||||
of the sized type class templates.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.integer.rationale"></a><a class="link" href="integer.html#boost_integer.integer.rationale" title="Rationale">Rationale</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The rationale for the design of the templates in this header includes:
|
||||
</p>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
||||
<li class="listitem">
|
||||
Avoid recursion because of concern about C++'s limited guaranteed recursion
|
||||
depth (17).
|
||||
</li>
|
||||
<li class="listitem">
|
||||
Avoid macros on general principles.
|
||||
</li>
|
||||
<li class="listitem">
|
||||
Try to keep the design as simple as possible.
|
||||
</li>
|
||||
</ul></div>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.integer.alternative"></a><a class="link" href="integer.html#boost_integer.integer.alternative" title="Alternative">Alternative</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
If the number of bits required is known beforehand, it may be more appropriate
|
||||
to use the types supplied in <a href="../../../../../boost/cstdint.hpp" target="_top"><boost/cstdint.hpp></a>.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.integer.credits"></a><a class="link" href="integer.html#boost_integer.integer.credits" title="Credits">Credits</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The author of most of the Boost integer type choosing templates is <a href="http://www.boost.org/people/beman_dawes.html" target="_top">Beman Dawes</a>. He
|
||||
gives thanks to Valentin Bonnard and <a href="http://www.boost.org/people/kevlin_henney.htm" target="_top">Kevlin
|
||||
Henney</a> for sharing their designs for similar templates. <a href="http://www.boost.org/people/daryle_walker.html" target="_top">Daryle
|
||||
Walker</a> designed the value-based sized templates.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><div class="copyright-footer">Copyright © 2001-2009 Beman
|
||||
Dawes, Daryle Walker, Gennaro Prota, John Maddock<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></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
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<a name="boost_integer.log2"></a><a class="link" href="log2.html" title="Compile Time log2 Calculation">Compile Time log2 Calculation</a>
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</h2></div></div></div>
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||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="log2.html#boost_integer.log2.synopsis">Synopsis</a></span></dt>
|
||||
<dt><span class="section"><a href="log2.html#boost_integer.log2.usage">Usage</a></span></dt>
|
||||
<dt><span class="section"><a href="log2.html#boost_integer.log2.demonstration_program">Demonstration
|
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Program</a></span></dt>
|
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<dt><span class="section"><a href="log2.html#boost_integer.log2.rationale">Rationale</a></span></dt>
|
||||
<dt><span class="section"><a href="log2.html#boost_integer.log2.credits">Credits</a></span></dt>
|
||||
</dl></div>
|
||||
<p>
|
||||
The class template in <a href="../../../../../boost/integer/static_log2.hpp" target="_top"><boost/integer/static_log2.hpp></a>
|
||||
determines the position of the highest bit in a given value. This facility
|
||||
is useful for solving generic programming problems.
|
||||
</p>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.log2.synopsis"></a><a class="link" href="log2.html#boost_integer.log2.synopsis" title="Synopsis">Synopsis</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span>
|
||||
<span class="special">{</span>
|
||||
|
||||
<span class="keyword">typedef</span> <span class="emphasis"><em>implementation-defined</em></span> <span class="identifier">static_log2_argument_type</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="emphasis"><em>implementation-defined</em></span> <span class="identifier">static_log2_result_type</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span><span class="identifier">static_log2_argument_type</span> <span class="identifier">arg</span><span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">static_log2</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">static_log2_result_type</span> <span class="identifier">value</span> <span class="special">=</span> <span class="emphasis"><em>implementation-defined</em></span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
||||
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">static_log2</span><span class="special"><</span> <span class="number">0</span> <span class="special">></span>
|
||||
<span class="special">{</span>
|
||||
<span class="comment">// The logarithm of zero is undefined.</span>
|
||||
<span class="special">};</span>
|
||||
|
||||
|
||||
<span class="special">}</span> <span class="comment">// namespace boost</span>
|
||||
</pre>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.log2.usage"></a><a class="link" href="log2.html#boost_integer.log2.usage" title="Usage">Usage</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The <code class="literal">boost::static_log2</code> class template takes one template
|
||||
parameter, a value of type <code class="literal">static_log2_argument_type</code>.
|
||||
The template only defines one member, <code class="literal">value</code>, which gives
|
||||
the truncated, base-two logarithm of the template argument.
|
||||
</p>
|
||||
<p>
|
||||
Since the logarithm of zero, for any base, is undefined, there is a specialization
|
||||
of <code class="literal">static_log2</code> for a template argument of zero. This specialization
|
||||
has no members, so an attempt to use the base-two logarithm of zero results
|
||||
in a compile-time error.
|
||||
</p>
|
||||
<p>
|
||||
Note:
|
||||
</p>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
||||
<li class="listitem">
|
||||
<code class="literal">static_log2_argument_type</code> is an <span class="emphasis"><em>unsigned
|
||||
integer type</em></span> (C++ standard, 3.9.1p3).
|
||||
</li>
|
||||
<li class="listitem">
|
||||
<code class="literal">static_log2_result_type</code> is an <span class="emphasis"><em>integer type</em></span>
|
||||
(C++ standard, 3.9.1p7).
|
||||
</li>
|
||||
</ul></div>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.log2.demonstration_program"></a><a class="link" href="log2.html#boost_integer.log2.demonstration_program" title="Demonstration Program">Demonstration
|
||||
Program</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The program <a href="../../../test/static_log2_test.cpp" target="_top">static_log2_test.cpp</a>
|
||||
is a simplistic demonstration of the results from instantiating various examples
|
||||
of the binary logarithm class template.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.log2.rationale"></a><a class="link" href="log2.html#boost_integer.log2.rationale" title="Rationale">Rationale</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The base-two (binary) logarithm, abbreviated lb, function is occasionally
|
||||
used to give order-estimates of computer algorithms. The truncated logarithm
|
||||
can be considered the highest power-of-two in a value, which corresponds
|
||||
to the value's highest set bit (for binary integers). Sometimes the highest-bit
|
||||
position could be used in generic programming, which requires the position
|
||||
to be available statically (<span class="emphasis"><em>i.e.</em></span> at compile-time).
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.log2.credits"></a><a class="link" href="log2.html#boost_integer.log2.credits" title="Credits">Credits</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The original version of the Boost binary logarithm class template was written
|
||||
by <a href="http://www.boost.org/people/daryle_walker.html" target="_top">Daryle Walker</a>
|
||||
and then enhanced by Giovanni Bajo with support for compilers without partial
|
||||
template specialization. The current version was suggested, together with
|
||||
a reference implementation, by Vesa Karvonen. Gennaro Prota wrote the actual
|
||||
source file.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><div class="copyright-footer">Copyright © 2001-2009 Beman
|
||||
Dawes, Daryle Walker, Gennaro Prota, John Maddock<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>
|
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<a name="boost_integer.mask"></a><a class="link" href="mask.html" title="Integer Masks">Integer Masks</a>
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</h2></div></div></div>
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<div class="toc"><dl class="toc">
|
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<dt><span class="section"><a href="mask.html#boost_integer.mask.overview">Overview</a></span></dt>
|
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|
||||
<dt><span class="section"><a href="mask.html#boost_integer.mask.single_bit_mask_class_template">Single
|
||||
Bit-Mask Class Template</a></span></dt>
|
||||
<dt><span class="section"><a href="mask.html#boost_integer.mask.group_bit_mask_class_template">Group
|
||||
Bit-Mask Class Template</a></span></dt>
|
||||
<dt><span class="section"><a href="mask.html#boost_integer.mask.implementation_notes">Implementation
|
||||
Notes</a></span></dt>
|
||||
<dt><span class="section"><a href="mask.html#boost_integer.mask.example">Example</a></span></dt>
|
||||
<dt><span class="section"><a href="mask.html#boost_integer.mask.demonstration_program">Demonstration
|
||||
Program</a></span></dt>
|
||||
<dt><span class="section"><a href="mask.html#boost_integer.mask.rationale">Rationale</a></span></dt>
|
||||
<dt><span class="section"><a href="mask.html#boost_integer.mask.credits">Credits</a></span></dt>
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||||
</dl></div>
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<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.mask.overview"></a><a class="link" href="mask.html#boost_integer.mask.overview" title="Overview">Overview</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The class templates in <a href="../../../../../boost/integer/integer_mask.hpp" target="_top"><boost/integer/integer_mask.hpp></a>
|
||||
provide bit masks for a certain bit position or a contiguous-bit pack of
|
||||
a certain size. The types of the masking constants come from the <a class="link" href="integer.html" title="Integer Type Selection">integer
|
||||
type selection templates</a> header.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.mask.synopsis"></a><a class="link" href="mask.html#boost_integer.mask.synopsis" title="Synopsis">Synopsis</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">cstddef</span><span class="special">></span> <span class="comment">// for std::size_t</span>
|
||||
|
||||
<span class="keyword">namespace</span> <span class="identifier">boost</span>
|
||||
<span class="special">{</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">Bit</span><span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">high_bit_mask_t</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">typedef</span> <span class="emphasis"><em>implementation-defined-type</em></span> <span class="identifier">least</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="emphasis"><em>implementation-defined-type</em></span> <span class="identifier">fast</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">least</span> <span class="identifier">high_bit</span> <span class="special">=</span> <span class="emphasis"><em>implementation-defined</em></span><span class="special">;</span>
|
||||
<span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">fast</span> <span class="identifier">high_bit_fast</span> <span class="special">=</span> <span class="emphasis"><em>implementation-defined</em></span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">bit_position</span> <span class="special">=</span> <span class="identifier">Bit</span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">Bits</span><span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">low_bits_mask_t</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">typedef</span> <span class="emphasis"><em>implementation-defined-type</em></span> <span class="identifier">least</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="emphasis"><em>implementation-defined-type</em></span> <span class="identifier">fast</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">least</span> <span class="identifier">sig_bits</span> <span class="special">=</span> <span class="emphasis"><em>implementation-defined</em></span><span class="special">;</span>
|
||||
<span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">fast</span> <span class="identifier">sig_bits_fast</span> <span class="special">=</span> <span class="emphasis"><em>implementation-defined</em></span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">bit_count</span> <span class="special">=</span> <span class="identifier">Bits</span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
||||
|
||||
<span class="comment">// Specializations for low_bits_mask_t exist for certain bit counts.</span>
|
||||
|
||||
<span class="special">}</span> <span class="comment">// namespace boost</span>
|
||||
</pre>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.mask.single_bit_mask_class_template"></a><a class="link" href="mask.html#boost_integer.mask.single_bit_mask_class_template" title="Single Bit-Mask Class Template">Single
|
||||
Bit-Mask Class Template</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The <code class="literal">boost::high_bit_mask_t</code> class template provides constants
|
||||
for bit masks representing the bit at a certain position. The masks are equivalent
|
||||
to the value 2<sup>Bit</sup>, where <code class="literal">Bit</code> is the template parameter.
|
||||
The bit position must be a nonnegative number from zero to <span class="emphasis"><em>Max</em></span>,
|
||||
where Max is one less than the number of bits supported by the largest unsigned
|
||||
built-in integral type. The following table describes the members of an instantiation
|
||||
of <code class="literal">high_bit_mask_t</code>.
|
||||
</p>
|
||||
<div class="table">
|
||||
<a name="boost_integer.mask.single_bit_mask_class_template.members_of_the__boost__high_bit_mask_t__class_template"></a><p class="title"><b>Table 2. Members of the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">high_bit_mask_t</span></code>
|
||||
Class Template</b></p>
|
||||
<div class="table-contents"><table class="table" summary="Members of the boost::high_bit_mask_t
|
||||
Class Template">
|
||||
<colgroup>
|
||||
<col>
|
||||
<col>
|
||||
</colgroup>
|
||||
<thead><tr>
|
||||
<th>
|
||||
<p>
|
||||
Member
|
||||
</p>
|
||||
</th>
|
||||
<th>
|
||||
<p>
|
||||
Meaning
|
||||
</p>
|
||||
</th>
|
||||
</tr></thead>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">least</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
The smallest, unsigned, built-in type that supports the given bit
|
||||
position.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">fast</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
The easiest-to-manipulate analog of <code class="literal">least</code>.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">high_bit</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
A <code class="literal">least</code> constant of the value 2<sup>Bit</sup>.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">high_bit_fast</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
A <code class="literal">fast</code> analog of <code class="literal">high_bit</code>.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">bit_position</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
The value of the template parameter, in case its needed from a
|
||||
renamed instantiation of the class template.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
</div>
|
||||
<br class="table-break">
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.mask.group_bit_mask_class_template"></a><a class="link" href="mask.html#boost_integer.mask.group_bit_mask_class_template" title="Group Bit-Mask Class Template">Group
|
||||
Bit-Mask Class Template</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The <code class="literal">boost::low_bits_mask_t</code> class template provides constants
|
||||
for bit masks equivalent to the value (2<sup>Bits</sup> - 1), where <code class="literal">Bits</code>
|
||||
is the template parameter. The parameter <code class="literal">Bits</code> must be
|
||||
a non-negative integer from zero to <span class="emphasis"><em>Max</em></span>, where Max is
|
||||
the number of bits supported by the largest, unsigned, built-in integral
|
||||
type. The following table describes the members of <code class="literal">low_bits_mask_t</code>.
|
||||
</p>
|
||||
<div class="table">
|
||||
<a name="boost_integer.mask.group_bit_mask_class_template.members_of_the___boost__low_bits_mask_t__class_template"></a><p class="title"><b>Table 3. Members of the <code class="literal">boost::low_bits_mask_t</code> Class Template</b></p>
|
||||
<div class="table-contents"><table class="table" summary="Members of the boost::low_bits_mask_t Class Template">
|
||||
<colgroup>
|
||||
<col>
|
||||
<col>
|
||||
</colgroup>
|
||||
<thead><tr>
|
||||
<th>
|
||||
<p>
|
||||
Member
|
||||
</p>
|
||||
</th>
|
||||
<th>
|
||||
<p>
|
||||
Meaning
|
||||
</p>
|
||||
</th>
|
||||
</tr></thead>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">least</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
The smallest, unsigned built-in type that supports the given bit
|
||||
count.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">fast</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
The easiest-to-manipulate analog of <code class="literal">least</code>.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">sig_bits</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
A <code class="literal">least</code> constant of the desired bit-masking
|
||||
value.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">sig_bits_fast</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
A <code class="literal">fast</code> analog of <code class="literal">sig_bits</code>.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">bit_count</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
The value of the template parameter, in case its needed from a
|
||||
renamed instantiation of the class template.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
</div>
|
||||
<br class="table-break">
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.mask.implementation_notes"></a><a class="link" href="mask.html#boost_integer.mask.implementation_notes" title="Implementation Notes">Implementation
|
||||
Notes</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
When <code class="literal">Bits</code> is the exact size of a built-in unsigned type,
|
||||
the implementation has to change to prevent undefined behavior. Therefore,
|
||||
there are specializations of <code class="literal">low_bits_mask_t</code> at those
|
||||
bit counts.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.mask.example"></a><a class="link" href="mask.html#boost_integer.mask.example" title="Example">Example</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">integer</span><span class="special">/</span><span class="identifier">integer_mask</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
|
||||
|
||||
<span class="comment">//...</span>
|
||||
|
||||
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">high_bit_mask_t</span><span class="special"><</span><span class="number">29</span><span class="special">></span> <span class="identifier">mask1_type</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">low_bits_mask_t</span><span class="special"><</span><span class="number">15</span><span class="special">></span> <span class="identifier">mask2_type</span><span class="special">;</span>
|
||||
|
||||
<span class="identifier">mask1_type</span><span class="special">::</span><span class="identifier">least</span> <span class="identifier">my_var1</span><span class="special">;</span>
|
||||
<span class="identifier">mask2_type</span><span class="special">::</span><span class="identifier">fast</span> <span class="identifier">my_var2</span><span class="special">;</span>
|
||||
<span class="comment">//...</span>
|
||||
|
||||
<span class="identifier">my_var1</span> <span class="special">|=</span> <span class="identifier">mask1_type</span><span class="special">::</span><span class="identifier">high_bit</span><span class="special">;</span>
|
||||
<span class="identifier">my_var2</span> <span class="special">&=</span> <span class="identifier">mask2_type</span><span class="special">::</span><span class="identifier">sig_bits_fast</span><span class="special">;</span>
|
||||
|
||||
<span class="comment">//...</span>
|
||||
<span class="special">}</span>
|
||||
</pre>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.mask.demonstration_program"></a><a class="link" href="mask.html#boost_integer.mask.demonstration_program" title="Demonstration Program">Demonstration
|
||||
Program</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The program <a href="../../../test/integer_mask_test.cpp" target="_top">integer_mask_test.cpp</a>
|
||||
is a simplistic demonstration of the results from instantiating various examples
|
||||
of the bit mask class templates.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.mask.rationale"></a><a class="link" href="mask.html#boost_integer.mask.rationale" title="Rationale">Rationale</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The class templates in this header are an extension of the <a class="link" href="integer.html" title="Integer Type Selection">integer
|
||||
type selection class templates</a>. The new class templates provide the
|
||||
same sized types, but also convenient masks to use when extracting the highest
|
||||
or all the significant bits when the containing built-in type contains more
|
||||
bits. This prevents contamination of values by the higher, unused bits.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.mask.credits"></a><a class="link" href="mask.html#boost_integer.mask.credits" title="Credits">Credits</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The author of the Boost bit mask class templates is <a href="http://www.boost.org/people/daryle_walker.html" target="_top">Daryle
|
||||
Walker</a>.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><div class="copyright-footer">Copyright © 2001-2009 Beman
|
||||
Dawes, Daryle Walker, Gennaro Prota, John Maddock<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></td>
|
||||
</tr></table>
|
||||
<hr>
|
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<div class="section">
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||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="boost_integer.minmax"></a><a class="link" href="minmax.html" title="Compile time min/max calculation">Compile time min/max calculation</a>
|
||||
</h2></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="minmax.html#boost_integer.minmax.synopsis">Synopsis</a></span></dt>
|
||||
<dt><span class="section"><a href="minmax.html#boost_integer.minmax.usage">Usage</a></span></dt>
|
||||
<dt><span class="section"><a href="minmax.html#boost_integer.minmax.example">Example</a></span></dt>
|
||||
<dt><span class="section"><a href="minmax.html#boost_integer.minmax.demonstration_program">Demonstration
|
||||
Program</a></span></dt>
|
||||
<dt><span class="section"><a href="minmax.html#boost_integer.minmax.rationale">Rationale</a></span></dt>
|
||||
<dt><span class="section"><a href="minmax.html#boost_integer.minmax.credits">Credits</a></span></dt>
|
||||
</dl></div>
|
||||
<p>
|
||||
The class templates in <a href="../../../../../boost/integer/static_min_max.hpp" target="_top"><boost/integer/static_min_max.hpp></a>
|
||||
provide a compile-time evaluation of the minimum or maximum of two integers.
|
||||
These facilities are useful for generic programming problems.
|
||||
</p>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.minmax.synopsis"></a><a class="link" href="minmax.html#boost_integer.minmax.synopsis" title="Synopsis">Synopsis</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span>
|
||||
<span class="special">{</span>
|
||||
|
||||
<span class="keyword">typedef</span> <span class="emphasis"><em>implementation-defined</em></span> <span class="identifier">static_min_max_signed_type</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="emphasis"><em>implementation-defined</em></span> <span class="identifier">static_min_max_unsigned_type</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span><span class="identifier">static_min_max_signed_type</span> <span class="identifier">Value1</span><span class="special">,</span> <span class="identifier">static_min_max_signed_type</span> <span class="identifier">Value2</span> <span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">static_signed_min</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span><span class="identifier">static_min_max_signed_type</span> <span class="identifier">Value1</span><span class="special">,</span> <span class="identifier">static_min_max_signed_type</span> <span class="identifier">Value2</span><span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">static_signed_max</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span><span class="identifier">static_min_max_unsigned_type</span> <span class="identifier">Value1</span><span class="special">,</span> <span class="identifier">static_min_max_unsigned_type</span> <span class="identifier">Value2</span><span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">static_unsigned_min</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span><span class="identifier">static_min_max_unsigned_type</span> <span class="identifier">Value1</span><span class="special">,</span> <span class="identifier">static_min_max_unsigned_type</span> <span class="identifier">Value2</span><span class="special">></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">static_unsigned_max</span><span class="special">;</span>
|
||||
|
||||
<span class="special">}</span>
|
||||
</pre>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.minmax.usage"></a><a class="link" href="minmax.html#boost_integer.minmax.usage" title="Usage">Usage</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The four class templates provide the combinations for finding the minimum
|
||||
or maximum of two <code class="literal">signed</code> or <code class="literal">unsigned</code>
|
||||
(<code class="literal">long</code>) parameters, <span class="emphasis"><em>Value1</em></span> and <span class="emphasis"><em>Value2</em></span>,
|
||||
at compile-time. Each template has a single static data member, <code class="literal">value</code>,
|
||||
which is set to the respective minimum or maximum of the template's parameters.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.minmax.example"></a><a class="link" href="minmax.html#boost_integer.minmax.example" title="Example">Example</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">integer</span><span class="special">/</span><span class="identifier">static_min_max</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
|
||||
|
||||
<span class="keyword">template</span> <span class="special"><</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="identifier">AddendSize1</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="identifier">AddendSize2</span> <span class="special">></span>
|
||||
<span class="keyword">class</span> <span class="identifier">adder</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">public</span><span class="special">:</span>
|
||||
<span class="keyword">static</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">const</span> <span class="identifier">addend1_size</span> <span class="special">=</span> <span class="identifier">AddendSize1</span><span class="special">;</span>
|
||||
<span class="keyword">static</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">const</span> <span class="identifier">addend2_size</span> <span class="special">=</span> <span class="identifier">AddendSize2</span><span class="special">;</span>
|
||||
<span class="keyword">static</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">const</span> <span class="identifier">sum_size</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">static_unsigned_max</span><span class="special"><</span><span class="identifier">AddendSize1</span><span class="special">,</span> <span class="identifier">AddendSize2</span><span class="special">>::</span><span class="identifier">value</span> <span class="special">+</span> <span class="number">1</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">typedef</span> <span class="keyword">int</span> <span class="identifier">addend1_type</span><span class="special">[</span> <span class="identifier">addend1_size</span> <span class="special">];</span>
|
||||
<span class="keyword">typedef</span> <span class="keyword">int</span> <span class="identifier">addend2_type</span><span class="special">[</span> <span class="identifier">addend2_size</span> <span class="special">];</span>
|
||||
<span class="keyword">typedef</span> <span class="keyword">int</span> <span class="identifier">sum_type</span><span class="special">[</span> <span class="identifier">sum_size</span> <span class="special">];</span>
|
||||
|
||||
<span class="keyword">void</span> <span class="keyword">operator</span> <span class="special">()(</span> <span class="identifier">addend1_type</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a1</span><span class="special">,</span> <span class="identifier">addend2_type</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">a2</span><span class="special">,</span> <span class="identifier">sum_type</span> <span class="special">&</span><span class="identifier">s</span> <span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
||||
|
||||
<span class="comment">//...</span>
|
||||
|
||||
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">int</span> <span class="keyword">const</span> <span class="identifier">a1</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">0</span><span class="special">,</span> <span class="number">4</span><span class="special">,</span> <span class="number">3</span> <span class="special">};</span> <span class="comment">// 340</span>
|
||||
<span class="keyword">int</span> <span class="keyword">const</span> <span class="identifier">a2</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">9</span><span class="special">,</span> <span class="number">8</span> <span class="special">};</span> <span class="comment">// 89</span>
|
||||
<span class="keyword">int</span> <span class="identifier">s</span><span class="special">[</span> <span class="number">4</span> <span class="special">];</span>
|
||||
<span class="identifier">adder</span><span class="special"><</span><span class="number">3</span><span class="special">,</span><span class="number">2</span><span class="special">></span> <span class="identifier">obj</span><span class="special">;</span>
|
||||
|
||||
<span class="identifier">obj</span><span class="special">(</span> <span class="identifier">a1</span><span class="special">,</span> <span class="identifier">a2</span><span class="special">,</span> <span class="identifier">s</span> <span class="special">);</span> <span class="comment">// 's' should be 429 or { 9, 2, 4, 0 }</span>
|
||||
<span class="comment">//...</span>
|
||||
<span class="special">}</span>
|
||||
</pre>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.minmax.demonstration_program"></a><a class="link" href="minmax.html#boost_integer.minmax.demonstration_program" title="Demonstration Program">Demonstration
|
||||
Program</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The program <a href="../../../test/static_min_max_test.cpp" target="_top">static_min_max_test.cpp</a>
|
||||
is a simplistic demonstration of various comparisons using the compile-time
|
||||
extrema class templates.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.minmax.rationale"></a><a class="link" href="minmax.html#boost_integer.minmax.rationale" title="Rationale">Rationale</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
Sometimes the minimum or maximum of several values needs to be found for
|
||||
later compile-time processing, <span class="emphasis"><em>e.g.</em></span> for a bound for
|
||||
another class template.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.minmax.credits"></a><a class="link" href="minmax.html#boost_integer.minmax.credits" title="Credits">Credits</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The author of the Boost compile-time extrema class templates is <a href="http://www.boost.org/people/daryle_walker.html" target="_top">Daryle
|
||||
Walker</a>.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><div class="copyright-footer">Copyright © 2001-2009 Beman
|
||||
Dawes, Daryle Walker, Gennaro Prota, John Maddock<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></td>
|
||||
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|
||||
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|
||||
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|
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|
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</h2></div></div></div>
|
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<div class="toc"><dl class="toc">
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||||
<dt><span class="section"><a href="mod_inverse.html#boost_integer.mod_inverse.introduction">Introduction</a></span></dt>
|
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<dt><span class="section"><a href="mod_inverse.html#boost_integer.mod_inverse.synopsis">Synopsis</a></span></dt>
|
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<dt><span class="section"><a href="mod_inverse.html#boost_integer.mod_inverse.usage">Usage</a></span></dt>
|
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<dt><span class="section"><a href="mod_inverse.html#boost_integer.mod_inverse.references">References</a></span></dt>
|
||||
</dl></div>
|
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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="boost_integer.mod_inverse.introduction"></a><a class="link" href="mod_inverse.html#boost_integer.mod_inverse.introduction" title="Introduction">Introduction</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The modular multiplicative inverse of a number <span class="emphasis"><em>a</em></span> is
|
||||
that number <span class="emphasis"><em>x</em></span> which satisfies <span class="emphasis"><em>ax</em></span>
|
||||
= 1 mod <span class="emphasis"><em>p</em></span>. A fast algorithm for computing modular multiplicative
|
||||
inverses based on the extended Euclidean algorithm exists and is provided
|
||||
by Boost.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.mod_inverse.synopsis"></a><a class="link" href="mod_inverse.html#boost_integer.mod_inverse.synopsis" title="Synopsis">Synopsis</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">integer</span><span class="special">/</span><span class="identifier">mod_inverse</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
|
||||
|
||||
<span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">integer</span> <span class="special">{</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">Z</span><span class="special">></span>
|
||||
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">optional</span><span class="special"><</span><span class="identifier">Z</span><span class="special">></span> <span class="identifier">mod_inverse</span><span class="special">(</span><span class="identifier">Z</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">Z</span> <span class="identifier">m</span><span class="special">);</span>
|
||||
|
||||
<span class="special">}}</span>
|
||||
</pre>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.mod_inverse.usage"></a><a class="link" href="mod_inverse.html#boost_integer.mod_inverse.usage" title="Usage">Usage</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
Multiplicative modular inverses exist if and only if <span class="emphasis"><em>a</em></span>
|
||||
and <span class="emphasis"><em>m</em></span> are coprime. So for example
|
||||
</p>
|
||||
<pre class="programlisting"><span class="keyword">auto</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">mod_inverse</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">5</span><span class="special">);</span>
|
||||
<span class="keyword">if</span> <span class="special">(</span><span class="identifier">x</span><span class="special">)</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">int</span> <span class="identifier">should_be_three</span> <span class="special">=</span> <span class="identifier">x</span><span class="special">.</span><span class="identifier">value</span><span class="special">();</span>
|
||||
<span class="special">}</span>
|
||||
<span class="keyword">auto</span> <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">mod_inverse</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">4</span><span class="special">);</span>
|
||||
<span class="keyword">if</span> <span class="special">(!</span><span class="identifier">y</span><span class="special">)</span>
|
||||
<span class="special">{</span>
|
||||
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"There is no inverse of 2 mod 4\n"</span><span class="special">;</span>
|
||||
<span class="special">}</span>
|
||||
</pre>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.mod_inverse.references"></a><a class="link" href="mod_inverse.html#boost_integer.mod_inverse.references" title="References">References</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
Wagstaff, Samuel S., <span class="emphasis"><em>The Joy of Factoring</em></span>, Vol. 68.
|
||||
American Mathematical Soc., 2013.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><div class="copyright-footer">Copyright © 2001-2009 Beman
|
||||
Dawes, Daryle Walker, Gennaro Prota, John Maddock<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></td>
|
||||
</tr></table>
|
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<div class="toc"><dl class="toc">
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<dt><span class="section"><a href="traits.html#boost_integer.traits.motivation">Motivation</a></span></dt>
|
||||
<dt><span class="section"><a href="traits.html#boost_integer.traits.synopsis">Synopsis</a></span></dt>
|
||||
<dt><span class="section"><a href="traits.html#boost_integer.traits.description">Description</a></span></dt>
|
||||
<dt><span class="section"><a href="traits.html#boost_integer.traits.test_program">Test Program</a></span></dt>
|
||||
<dt><span class="section"><a href="traits.html#boost_integer.traits.acknowledgements">Acknowledgements</a></span></dt>
|
||||
</dl></div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.traits.motivation"></a><a class="link" href="traits.html#boost_integer.traits.motivation" title="Motivation">Motivation</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The C++ Standard Library <limits> header supplies a class template
|
||||
<code class="computeroutput"><span class="identifier">numeric_limits</span><span class="special"><></span></code>
|
||||
with specializations for each fundamental type.
|
||||
</p>
|
||||
<p>
|
||||
For integer types, the interesting members of <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><></span></code> are:
|
||||
</p>
|
||||
<pre class="programlisting"><span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">bool</span> <span class="identifier">is_specialized</span><span class="special">;</span> <span class="comment">// Will be true for integer types.</span>
|
||||
<span class="keyword">static</span> <span class="identifier">T</span> <span class="identifier">min</span><span class="special">()</span> <span class="keyword">throw</span><span class="special">();</span> <span class="comment">// Smallest representable value.</span>
|
||||
<span class="keyword">static</span> <span class="identifier">T</span> <span class="identifier">max</span><span class="special">()</span> <span class="keyword">throw</span><span class="special">();</span> <span class="comment">// Largest representable value.</span>
|
||||
<span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">int</span> <span class="identifier">digits</span><span class="special">;</span> <span class="comment">// For integers, the number of value bits.</span>
|
||||
<span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">int</span> <span class="identifier">digits10</span><span class="special">;</span> <span class="comment">// The number of base 10 digits that can be represented.</span>
|
||||
<span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">bool</span> <span class="identifier">is_signed</span><span class="special">;</span> <span class="comment">// True if the type is signed.</span>
|
||||
<span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">bool</span> <span class="identifier">is_integer</span><span class="special">;</span> <span class="comment">// Will be true for all integer types.</span>
|
||||
</pre>
|
||||
<p>
|
||||
For many uses, these are sufficient. But min() and max() are problematical
|
||||
because they are not constant expressions (std::5.19), yet some usages require
|
||||
constant expressions.
|
||||
</p>
|
||||
<p>
|
||||
The template class <code class="literal">integer_traits</code> addresses this problem.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.traits.synopsis"></a><a class="link" href="traits.html#boost_integer.traits.synopsis" title="Synopsis">Synopsis</a>
|
||||
</h3></div></div></div>
|
||||
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</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">class</span> <span class="identifier">integer_traits</span> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">public</span><span class="special">:</span>
|
||||
<span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">bool</span> <span class="identifier">is_integral</span> <span class="special">=</span> <span class="keyword">false</span><span class="special">;</span>
|
||||
<span class="comment">//</span>
|
||||
<span class="comment">// These members are defined only if T is a built-in</span>
|
||||
<span class="comment">// integal type:</span>
|
||||
<span class="comment">//</span>
|
||||
<span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">const_min</span> <span class="special">=</span> <span class="emphasis"><em>implementation-defined</em></span><span class="special">;</span>
|
||||
<span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">const_max</span> <span class="special">=</span> <span class="emphasis"><em>implementation-defined</em></span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
||||
<span class="special">}</span>
|
||||
</pre>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.traits.description"></a><a class="link" href="traits.html#boost_integer.traits.description" title="Description">Description</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
Template class <code class="literal">integer_traits</code> is derived from <code class="literal">std::numeric_limits</code>.
|
||||
The primary specialization adds the single <code class="literal">bool</code> member
|
||||
<code class="literal">is_integral</code> with the compile-time constant value <code class="literal">false</code>.
|
||||
However, for all integral types <code class="literal">T</code> (std::3.9.1/7 [basic.fundamental]),
|
||||
there are specializations provided with the following compile-time constants
|
||||
defined:
|
||||
</p>
|
||||
<div class="informaltable"><table class="table">
|
||||
<colgroup>
|
||||
<col>
|
||||
<col>
|
||||
<col>
|
||||
</colgroup>
|
||||
<thead><tr>
|
||||
<th>
|
||||
<p>
|
||||
member
|
||||
</p>
|
||||
</th>
|
||||
<th>
|
||||
<p>
|
||||
type
|
||||
</p>
|
||||
</th>
|
||||
<th>
|
||||
<p>
|
||||
value
|
||||
</p>
|
||||
</th>
|
||||
</tr></thead>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">is_integral</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
bool
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">true</code>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">const_min</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">T</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
equivalent to <code class="literal">std::numeric_limits<T>::min()</code>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">const_max</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">T</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
equivalent to <code class="literal">std::numeric_limits<T>::max()</code>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
Note: The <span class="emphasis"><em>is_integral</em></span> flag is provided, because a user-defined
|
||||
integer class should specialize <code class="literal">std::numeric_limits<>::is_integer
|
||||
= true</code>, while compile-time constants <code class="literal">const_min</code>
|
||||
and <code class="literal">const_max</code> are not provided for that user-defined class,
|
||||
unless boost::integer_traits is also specialized.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.traits.test_program"></a><a class="link" href="traits.html#boost_integer.traits.test_program" title="Test Program">Test Program</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
The program <code class="literal"><a href="../../../test/integer_traits_test.cpp" target="_top">integer_traits_test.cpp</a></code>
|
||||
exercises the <code class="literal">integer_traits</code> class.
|
||||
</p>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_integer.traits.acknowledgements"></a><a class="link" href="traits.html#boost_integer.traits.acknowledgements" title="Acknowledgements">Acknowledgements</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
Beman Dawes, Ed Brey, Steve Cleary, and Nathan Myers discussed the integer
|
||||
traits idea on the boost mailing list in August 1999.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><div class="copyright-footer">Copyright © 2001-2009 Beman
|
||||
Dawes, Daryle Walker, Gennaro Prota, John Maddock<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></td>
|
||||
</tr></table>
|
||||
<hr>
|
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<div class="spirit-nav">
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<a accesskey="p" href="../index.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="integer.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
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<div><h2 class="title">
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<a name="boost_integer"></a>Boost.Integer</h2></div>
|
||||
<div><div class="authorgroup">
|
||||
<div class="author"><h3 class="author">
|
||||
<span class="firstname">Beman</span> <span class="surname">Dawes</span>
|
||||
</h3></div>
|
||||
<div class="author"><h3 class="author">
|
||||
<span class="firstname">Daryle</span> <span class="surname">Walker</span>
|
||||
</h3></div>
|
||||
<div class="author"><h3 class="author">
|
||||
<span class="firstname">Gennaro</span> <span class="surname">Prota</span>
|
||||
</h3></div>
|
||||
<div class="author"><h3 class="author">
|
||||
<span class="firstname">John</span> <span class="surname">Maddock</span>
|
||||
</h3></div>
|
||||
</div></div>
|
||||
<div><p class="copyright">Copyright © 2001-2009 Beman
|
||||
Dawes, Daryle Walker, Gennaro Prota, John Maddock</p></div>
|
||||
<div><div class="legalnotice">
|
||||
<a name="boost_integer.legal"></a><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></div>
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</div>
|
||||
<hr>
|
||||
</div>
|
||||
<div class="toc">
|
||||
<p><b>Table of Contents</b></p>
|
||||
<dl class="toc">
|
||||
<dt><span class="section"><a href="index.html#boost_integer.overview">Overview</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_integer/traits.html">Integer Traits</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_integer/integer.html">Integer Type Selection</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_integer/gcd_lcm.html">Greatest Common Divisor and Least
|
||||
Common Multiple</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_integer/extended_euclidean.html">Extended Euclidean Algorithm</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_integer/mod_inverse.html">Modular Multiplicative Inverse</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_integer/mask.html">Integer Masks</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_integer/log2.html">Compile Time log2 Calculation</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_integer/minmax.html">Compile time min/max calculation</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_integer/history.html">History</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_integer/cstdint.html">Removed from library: Standard Integer
|
||||
Types</a></span></dt>
|
||||
</dl>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
|
||||
<a name="boost_integer.overview"></a><a class="link" href="index.html#boost_integer.overview" title="Overview">Overview</a>
|
||||
</h2></div></div></div>
|
||||
<p>
|
||||
Boost.Integer provides integer type support, particularly helpful in generic
|
||||
programming. It provides the means to select an integer type based upon its
|
||||
properties, like the number of bits or the maximum supported value, as well
|
||||
as compile-time bit mask selection. There is a derivative of std::numeric_limits
|
||||
that provides integral constant expressions for <code class="computeroutput"><span class="identifier">min</span></code>
|
||||
and <code class="computeroutput"><span class="identifier">max</span></code>. Finally, it provides
|
||||
two compile-time algorithms: determining the highest power of two in a compile-time
|
||||
value; and computing min and max of constant expressions.
|
||||
</p>
|
||||
<div class="informaltable"><table class="table">
|
||||
<colgroup>
|
||||
<col>
|
||||
<col>
|
||||
<col>
|
||||
</colgroup>
|
||||
<thead><tr>
|
||||
<th>
|
||||
<p>
|
||||
Component
|
||||
</p>
|
||||
</th>
|
||||
<th>
|
||||
<p>
|
||||
Header
|
||||
</p>
|
||||
</th>
|
||||
<th>
|
||||
<p>
|
||||
Purpose
|
||||
</p>
|
||||
</th>
|
||||
</tr></thead>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Forward Declarations.
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal"><a href="../../../../boost/integer_fwd.hpp" target="_top"><boost/integer_fwd.hpp></a></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Forward declarations of classes and class templates - for use when
|
||||
just the name of a class is needed.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<a class="link" href="boost_integer/traits.html" title="Integer Traits">Integer Traits</a>.
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal"><a href="../../../../boost/integer_traits.hpp" target="_top"><boost/integer_traits.hpp></a></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Class template <code class="literal">boost::integer_traits</code>, derives
|
||||
from <code class="literal">std::numeric_limits</code> and adds <code class="literal">const_min</code>
|
||||
and <code class="literal">const_max</code> members.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<a class="link" href="boost_integer/integer.html" title="Integer Type Selection">Integer Type Selection</a>.
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal"><a href="../../../../boost/integer.hpp" target="_top"><boost/integer.hpp></a></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Templates for integer type selection based on properties such as
|
||||
maximum value or number of bits: Use to select the type of an integer
|
||||
when some property such as maximum value or number of bits is known.
|
||||
Useful for generic programming.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<a class="link" href="boost_integer/gcd_lcm.html" title="Greatest Common Divisor and Least Common Multiple">Greatest Common Divisor and
|
||||
Least Common Multiple</a>.
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal"><a href="../../../../boost/integer/common_factor_rt.hpp" target="_top"><boost/integer/common_factor_rt.hpp></a></code>
|
||||
and <code class="literal"><a href="../../../../boost/integer/common_factor_ct.hpp" target="_top"><boost/integer/common_factor_ct.hpp></a></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Functions <code class="computeroutput"><span class="identifier">gcd</span></code> and
|
||||
<code class="computeroutput"><span class="identifier">lcm</span></code> plus function
|
||||
objects and compile time versions.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<a class="link" href="boost_integer/mask.html" title="Integer Masks">Integer Masks</a>.
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal"><a href="../../../../boost/integer/integer_mask.hpp" target="_top"><boost/integer/integer_mask.hpp></a></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Templates for the selection of integer masks, single or lowest group,
|
||||
based on the number of bits: Use to select a particular mask when
|
||||
the bit position(s) are based on a compile-time variable. Useful
|
||||
for generic programming.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<a class="link" href="boost_integer/log2.html" title="Compile Time log2 Calculation">Compile time log2 Calculation</a>.
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal"><a href="../../../../boost/integer/static_log2.hpp" target="_top"><boost/integer/static_log2.hpp></a></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Template for finding the highest power of two in a number: Use to
|
||||
find the bit-size/range based on a maximum value. Useful for generic
|
||||
programming.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<a class="link" href="boost_integer/minmax.html" title="Compile time min/max calculation">Compile time min/max calculation</a>.
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal"><a href="../../../../boost/integer/static_min_max.hpp" target="_top"><boost/integer/static_min_max.hpp></a></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Templates for finding the extrema of two numbers: Use to find a bound
|
||||
based on a minimum or maximum value. Useful for generic programming.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<a class="link" href="boost_integer/extended_euclidean.html" title="Extended Euclidean Algorithm">Extended Euclidean
|
||||
algorithm</a>.
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal"><a href="../../../../boost/integer/extended_euclidean.hpp" target="_top"><boost/integer/extended_euclidean.hpp></a></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Solves <span class="emphasis"><em>mx + ny = gcd(x,y)</em></span> for <span class="emphasis"><em>x</em></span>
|
||||
and <span class="emphasis"><em>y</em></span>.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<a class="link" href="boost_integer/mod_inverse.html" title="Modular Multiplicative Inverse">Modular multiplicative
|
||||
inverse</a>.
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal"><a href="../../../../boost/integer/mod_inverse.hpp" target="_top"><boost/integer/mod_inverse.hpp></a></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Given <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>m</em></span>, solves
|
||||
<span class="emphasis"><em>ax</em></span> = 1 mod <span class="emphasis"><em>m</em></span> for <span class="emphasis"><em>x</em></span>.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
</div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"><p><small>Last revised: November 02, 2018 at 19:38:28 GMT</small></p></td>
|
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