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<div class="titlepage"><div><div><h3 class="title">
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<a name="math_toolkit.internals.engel_expansion"></a><a class="link" href="engel_expansion.html" title="Engel Expansion">Engel Expansion</a>
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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">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">engel_expansion</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="identifier">math</span><span class="special">::</span><span class="identifier">tools</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">Real</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">Z</span> <span class="special">=</span> <span class="identifier">int64_t</span><span class="special">></span>
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<span class="keyword">class</span> <span class="identifier">engel_expansion</span> <span class="special">{</span>
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<span class="keyword">public</span><span class="special">:</span>
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<span class="identifier">engel_expansion</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">);</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="identifier">Z</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">digits</span><span class="special">()</span> <span class="keyword">const</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">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">Z_</span><span class="special">></span>
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<span class="keyword">friend</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="keyword">operator</span><span class="special"><<(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="identifier">out</span><span class="special">,</span> <span class="identifier">engel_expansion</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">Z</span><span class="special">>&</span> <span class="identifier">engel</span><span class="special">);</span>
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<span class="special">};</span>
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<span class="special">}</span>
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</pre>
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<p>
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The <code class="computeroutput"><span class="identifier">engel_expansion</span></code> class
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provided by Boost converts a floating point number into an <a href="https://en.wikipedia.org/wiki/Engel_expansion" target="_top">Engel
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series</a>.
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</p>
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<p>
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Here's a minimal working example:
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</p>
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<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">e</span><span class="special">;</span>
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<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">::</span><span class="identifier">engel_expansion</span><span class="special">;</span>
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<span class="keyword">auto</span> <span class="identifier">engel</span> <span class="special">=</span> <span class="identifier">engel_expansion</span><span class="special">(</span><span class="identifier">e</span><span class="special"><</span><span class="keyword">double</span><span class="special">>());</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"e ≈ "</span> <span class="special"><<</span> <span class="identifier">engel</span> <span class="special"><<</span> <span class="string">"\n"</span><span class="special">;</span>
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<span class="comment">// Prints:</span>
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<span class="comment">// e ≈ {1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}</span>
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</pre>
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<p>
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The digits of an Engel expansion tend to grow exponentially, so the integer
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template option might need to be utilized. For example, we can use a wider
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integer type via
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</p>
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<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">checked_int1024_t</span><span class="special">;</span>
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<span class="keyword">auto</span> <span class="identifier">engel</span> <span class="special">=</span> <span class="identifier">engel_expansion</span><span class="special"><</span><span class="identifier">__float128</span><span class="special">,</span> <span class="identifier">checked_int1024_t</span><span class="special">>(</span><span class="identifier">pi</span><span class="special"><</span><span class="identifier">__float128</span><span class="special">>());</span>
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</pre>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Walker and Xiaogang Zhang<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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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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