[DEV] add v1.76.0

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2021-10-05 21:37:46 +02:00
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<td align="right"><div class="copyright-footer">Copyright &#169; 2001-2009 Beman
<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>)
file LICENSE_1_0.txt or copy at <a href="https://www.boost.org/LICENSE_1_0.txt" target="_top">https://www.boost.org/LICENSE_1_0.txt</a>)
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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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<div class="toc"><dl class="toc">
<dt><span class="section"><a href="extended_euclidean.html#boost_integer.extended_euclidean.introduction">Introduction</a></span></dt>
<dt><span class="section"><a href="extended_euclidean.html#boost_integer.extended_euclidean.synopsis">Synopsis</a></span></dt>
<dt><span class="section"><a href="extended_euclidean.html#boost_integer.extended_euclidean.usage">Usage</a></span></dt>
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<div class="titlepage"><div><div><h3 class="title">
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</h3></div></div></div>
<p>
The extended Euclidean algorithm solves the integer relation <span class="emphasis"><em>mx
+ ny</em></span> = gcd(<span class="emphasis"><em>m</em></span>, <span class="emphasis"><em>n</em></span>) for
<span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>.
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</h3></div></div></div>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">integer</span><span class="special">/</span><span class="identifier">extended_euclidean</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</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">&lt;</span><span class="keyword">class</span> <span class="identifier">Z</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">euclidean_result_t</span> <span class="special">{</span>
<span class="identifier">Z</span> <span class="identifier">gcd</span><span class="special">;</span>
<span class="identifier">Z</span> <span class="identifier">x</span><span class="special">;</span>
<span class="identifier">Z</span> <span class="identifier">y</span><span class="special">;</span>
<span class="special">};</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Z</span><span class="special">&gt;</span>
<span class="identifier">euclidean_result_t</span><span class="special">&lt;</span><span class="identifier">Z</span><span class="special">&gt;</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>
<span class="special">}}</span>
</pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_integer.extended_euclidean.usage"></a><a class="link" href="extended_euclidean.html#boost_integer.extended_euclidean.usage" title="Usage">Usage</a>
</h3></div></div></div>
<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>
<span class="keyword">int</span> <span class="identifier">n</span> <span class="special">=</span> <span class="number">15</span><span class="special">;</span>
<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>
<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>
<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>
<span class="comment">// mx + ny = gcd(m,n) should now hold</span>
</pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_integer.extended_euclidean.references"></a><a class="link" href="extended_euclidean.html#boost_integer.extended_euclidean.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="https://www.boost.org/LICENSE_1_0.txt" target="_top">https://www.boost.org/LICENSE_1_0.txt</a>)
</p>
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@@ -38,7 +38,7 @@
Determination</a></span></dt>
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.compile_time">Compile time GCD
and LCM determination</a></span></dt>
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_header">Header &lt;boost/math/common_factor.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_header">Header &lt;boost/integer/common_factor.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.demo">Demonstration Program</a></span></dt>
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.rationale">Rationale</a></span></dt>
<dt><span class="section"><a href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_history">History</a></span></dt>
@@ -61,7 +61,7 @@
</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">math</span>
<span class="keyword">namespace</span> <span class="identifier">integer</span>
<span class="special">{</span>
<span class="keyword">template</span> <span class="special">&lt;</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">&gt;</span>
@@ -102,10 +102,10 @@
Object</a>
</h3></div></div></div>
<p>
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/math/common_factor_rt.hpp" target="_top">&lt;boost/math/common_factor_rt.hpp&gt;</a>
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/integer/common_factor_rt.hpp" target="_top">&lt;boost/integer/common_factor_rt.hpp&gt;</a>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">gcd_evaluator</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>
@@ -120,11 +120,11 @@
<span class="special">};</span>
</pre>
<p>
The boost::math::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.
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
@@ -144,10 +144,10 @@
Object</a>
</h3></div></div></div>
<p>
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/math/common_factor_rt.hpp" target="_top">&lt;boost/math/common_factor_rt.hpp&gt;</a>
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/integer/common_factor_rt.hpp" target="_top">&lt;boost/integer/common_factor_rt.hpp&gt;</a>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">lcm_evaluator</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>
@@ -162,13 +162,13 @@
<span class="special">};</span>
</pre>
<p>
The boost::math::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.
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
@@ -188,13 +188,13 @@
Determination</a>
</h3></div></div></div>
<p>
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/math/common_factor_rt.hpp" target="_top">&lt;boost/math/common_factor_rt.hpp&gt;</a>
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/integer/common_factor_rt.hpp" target="_top">&lt;boost/integer/common_factor_rt.hpp&gt;</a>
</p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">&gt;</span>
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</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">&amp;</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="identifier">b</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">&amp;</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="identifier">b</span> <span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</span> <span class="keyword">typename</span> <span class="identifier">IntegerType</span> <span class="special">&gt;</span>
<span class="keyword">constexpr</span> <span class="identifier">IntegerType</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</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">&amp;</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="identifier">b</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">&amp;</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="identifier">b</span> <span class="special">);</span>
<span class="keyword">template</span> <span class="special">&lt;</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">&gt;</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">&amp;</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">IntegerType</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">Args</span> <span class="keyword">const</span><span class="special">&amp;...</span> <span class="special">);</span>
@@ -211,8 +211,8 @@
<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::math::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">math</span><span class="special">::</span><span class="identifier">gcd_range</span></code>
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
@@ -222,7 +222,7 @@
to reach unity.
</p>
<p>
The boost::math::lcm function template returns the least common (nonnegative)
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>
@@ -249,17 +249,17 @@
</p></td></tr>
</table></div>
<p>
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/math/common_factor_ct.hpp" target="_top">&lt;boost/math/common_factor_ct.hpp&gt;</a>
<span class="bold"><strong>Header: </strong></span> <a href="../../../../../boost/integer/common_factor_ct.hpp" target="_top">&lt;boost/integer/common_factor_ct.hpp&gt;</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">&lt;</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">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</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">&lt;</span><span class="identifier">static_gcd_type</span><span class="special">,</span> <span class="identifier">implementation_defined</span><span class="special">&gt;</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">&lt;</span><span class="identifier">static_gcd_type</span><span class="special">,</span> <span class="identifier">implementation_defined</span><span class="special">&gt;</span>
<span class="special">{</span>
<span class="special">};</span>
<span class="keyword">template</span> <span class="special">&lt;</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">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</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">&lt;</span><span class="identifier">static_gcd_type</span><span class="special">,</span> <span class="identifier">implementation_defined</span><span class="special">&gt;</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">&lt;</span><span class="identifier">static_gcd_type</span><span class="special">,</span> <span class="identifier">implementation_defined</span><span class="special">&gt;</span>
<span class="special">{</span>
<span class="special">};</span>
</pre>
@@ -271,8 +271,8 @@
<span class="keyword">long</span></code> for some older compilers.
</p>
<p>
The boost::math::static_gcd and boost::math::static_lcm class templates take
two value-based template parameters of the <span class="emphasis"><em>static_gcd_type</em></span>
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.
@@ -283,7 +283,7 @@
<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">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">common_factor</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">integer</span><span class="special">/</span><span class="identifier">common_factor</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">algorithm</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iterator</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
@@ -294,29 +294,29 @@
<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">&lt;&lt;</span> <span class="string">"The GCD and LCM of 6 and 15 are "</span>
<span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</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">&lt;&lt;</span> <span class="string">" and "</span>
<span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</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">&lt;&lt;</span> <span class="string">", respectively."</span>
<span class="special">&lt;&lt;</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">&lt;&lt;</span> <span class="string">" and "</span>
<span class="special">&lt;&lt;</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">&lt;&lt;</span> <span class="string">", respectively."</span>
<span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"The GCD and LCM of 8 and 9 are "</span>
<span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">static_gcd</span><span class="special">&lt;</span><span class="number">8</span><span class="special">,</span> <span class="number">9</span><span class="special">&gt;::</span><span class="identifier">value</span>
<span class="special">&lt;&lt;</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">&lt;</span><span class="number">8</span><span class="special">,</span> <span class="number">9</span><span class="special">&gt;::</span><span class="identifier">value</span>
<span class="special">&lt;&lt;</span> <span class="string">" and "</span>
<span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">static_lcm</span><span class="special">&lt;</span><span class="number">8</span><span class="special">,</span> <span class="number">9</span><span class="special">&gt;::</span><span class="identifier">value</span>
<span class="special">&lt;&lt;</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">&lt;</span><span class="number">8</span><span class="special">,</span> <span class="number">9</span><span class="special">&gt;::</span><span class="identifier">value</span>
<span class="special">&lt;&lt;</span> <span class="string">", respectively."</span> <span class="special">&lt;&lt;</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">math</span><span class="special">::</span><span class="identifier">gcd_evaluator</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;()</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">&lt;</span><span class="keyword">int</span><span class="special">&gt;()</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">&lt;</span><span class="keyword">int</span><span class="special">&gt;(</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 &lt;boost/math/common_factor.hpp&gt;">Header &lt;boost/math/common_factor.hpp&gt;</a>
<a name="boost_integer.gcd_lcm.gcd_header"></a><a class="link" href="gcd_lcm.html#boost_integer.gcd_lcm.gcd_header" title="Header &lt;boost/integer/common_factor.hpp&gt;">Header &lt;boost/integer/common_factor.hpp&gt;</a>
</h3></div></div></div>
<p>
This header simply includes the headers <a href="../../../../../boost/math/common_factor_ct.hpp" target="_top">&lt;boost/math/common_factor_ct.hpp&gt;</a>
and <a href="../../../../../boost/math/common_factor_rt.hpp" target="_top">&lt;boost/math/common_factor_rt.hpp&gt;</a>.
This header simply includes the headers <a href="../../../../../boost/integer/common_factor_ct.hpp" target="_top">&lt;boost/integer/common_factor_ct.hpp&gt;</a>
and <a href="../../../../../boost/integer/common_factor_rt.hpp" target="_top">&lt;boost/integer/common_factor_rt.hpp&gt;</a>.
</p>
<p>
Note this is a legacy header: it used to contain the actual implementation,
@@ -329,7 +329,7 @@
<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/math/test/common_factor_test.cpp" target="_top">common_factor_test.cpp</a>
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
@@ -344,7 +344,7 @@
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
maintainence.
maintenance.
</p>
</div>
<div class="section">
@@ -385,16 +385,16 @@
</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 &#169; 2001-2009 Beman
<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>)
file LICENSE_1_0.txt or copy at <a href="https://www.boost.org/LICENSE_1_0.txt" target="_top">https://www.boost.org/LICENSE_1_0.txt</a>)
</p>
</div></td>
</tr></table>
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<a accesskey="p" href="integer.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="mask.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
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@@ -1,6 +1,6 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>History</title>
<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
@@ -75,10 +75,10 @@
</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 &#169; 2001-2009 Beman
<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>)
file LICENSE_1_0.txt or copy at <a href="https://www.boost.org/LICENSE_1_0.txt" target="_top">https://www.boost.org/LICENSE_1_0.txt</a>)
</p>
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@@ -1,6 +1,6 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Integer Type Selection</title>
<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
@@ -139,7 +139,7 @@
<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&#160;1.&#160;Criteria for the Sized Type Class Templates</b></p>
<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>
@@ -353,10 +353,10 @@
<span class="special">{</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">int_t</span><span class="special">&lt;</span><span class="number">24</span><span class="special">&gt;::</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 guarenteed not to be truncated:</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">&lt;</span><span class="number">1000</span><span class="special">&gt;::</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 guarenteed not to be truncated, and as fast</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">&lt;</span><span class="number">1000</span><span class="special">&gt;::</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>
@@ -408,19 +408,19 @@
<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
The author of most of the Boost integer type choosing templates is <a href="https://www.boost.org/people/beman_dawes.html" target="_top">Beman Dawes</a>.
He gives thanks to Valentin Bonnard and <a href="https://www.boost.org/people/kevlin_henney.htm" target="_top">Kevlin
Henney</a> for sharing their designs for similar templates. <a href="https://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 &#169; 2001-2009 Beman
<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>)
file LICENSE_1_0.txt or copy at <a href="https://www.boost.org/LICENSE_1_0.txt" target="_top">https://www.boost.org/LICENSE_1_0.txt</a>)
</p>
</div></td>
</tr></table>

View File

@@ -1,6 +1,6 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Compile Time log2 Calculation</title>
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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
@@ -126,7 +126,7 @@
</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>
by <a href="https://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
@@ -136,10 +136,10 @@
</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 &#169; 2001-2009 Beman
<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>)
file LICENSE_1_0.txt or copy at <a href="https://www.boost.org/LICENSE_1_0.txt" target="_top">https://www.boost.org/LICENSE_1_0.txt</a>)
</p>
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@@ -1,12 +1,12 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Integer Masks</title>
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@@ -20,7 +20,7 @@
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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
@@ -105,7 +105,7 @@
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&#160;2.&#160;Members of the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">high_bit_mask_t</span></code>
<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">
@@ -207,7 +207,7 @@
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&#160;3.&#160;Members of the <code class="literal">boost::low_bits_mask_t</code> Class Template</b></p>
<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>
@@ -358,23 +358,23 @@
<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
The author of the Boost bit mask class templates is <a href="https://www.boost.org/people/daryle_walker.html" target="_top">Daryle
Walker</a>.
</p>
</div>
</div>
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<td align="right"><div class="copyright-footer">Copyright &#169; 2001-2009 Beman
<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>)
file LICENSE_1_0.txt or copy at <a href="https://www.boost.org/LICENSE_1_0.txt" target="_top">https://www.boost.org/LICENSE_1_0.txt</a>)
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</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
The author of the Boost compile-time extrema class templates is <a href="https://www.boost.org/people/daryle_walker.html" target="_top">Daryle
Walker</a>.
</p>
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<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001-2009 Beman
<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>)
file LICENSE_1_0.txt or copy at <a href="https://www.boost.org/LICENSE_1_0.txt" target="_top">https://www.boost.org/LICENSE_1_0.txt</a>)
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_integer.mod_inverse"></a><a class="link" href="mod_inverse.html" title="Modular Multiplicative Inverse">Modular Multiplicative Inverse</a>
</h2></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="mod_inverse.html#boost_integer.mod_inverse.introduction">Introduction</a></span></dt>
<dt><span class="section"><a href="mod_inverse.html#boost_integer.mod_inverse.synopsis">Synopsis</a></span></dt>
<dt><span class="section"><a href="mod_inverse.html#boost_integer.mod_inverse.usage">Usage</a></span></dt>
<dt><span class="section"><a href="mod_inverse.html#boost_integer.mod_inverse.references">References</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<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">&lt;</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">&gt;</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">&lt;</span><span class="keyword">class</span> <span class="identifier">Z</span><span class="special">&gt;</span>
<span class="identifier">Z</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>
<pre class="programlisting"><span class="keyword">int</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="comment">// prints x = 3:</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"x = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">x</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
<span class="keyword">int</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="number">0</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">&lt;&lt;</span> <span class="string">"There is no inverse of 2 mod 4\n"</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<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. If <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>m</em></span>
share a common factor, then <code class="computeroutput"><span class="identifier">mod_inverse</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span>
<span class="identifier">m</span><span class="special">)</span></code>
returns zero.
</p>
</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="https://www.boost.org/LICENSE_1_0.txt" target="_top">https://www.boost.org/LICENSE_1_0.txt</a>)
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<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001-2009 Beman
<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>)
file LICENSE_1_0.txt or copy at <a href="https://www.boost.org/LICENSE_1_0.txt" target="_top">https://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -37,12 +37,12 @@
<span class="firstname">John</span> <span class="surname">Maddock</span>
</h3></div>
</div></div>
<div><p class="copyright">Copyright &#169; 2001-2009 Beman
<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>)
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@@ -56,6 +56,8 @@
<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>
@@ -237,12 +239,50 @@
</p>
</td>
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<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">&lt;boost/integer/extended_euclidean.hpp&gt;</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>
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<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">&lt;boost/integer/mod_inverse.hpp&gt;</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>
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<td align="left"><p><small>Last revised: December 14, 2017 at 00:16:53 GMT</small></p></td>
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