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<title>Calculating the Representation Distance Between Two floating-point Values (ULP) float_distance</title>
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<div class="titlepage"><div><div><h3 class="title">
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<a name="math_toolkit.next_float.float_distance"></a><a class="link" href="float_distance.html" title="Calculating the Representation Distance Between Two floating-point Values (ULP) float_distance">Calculating the
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Representation Distance Between Two floating-point Values (ULP) float_distance</a>
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</h3></div></div></div>
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<p>
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Function float_distance finds the number of gaps/bits/ULP between any two
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floating-point values. If the significands of floating-point numbers are
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viewed as integers, then their difference is the number of ULP/gaps/bits
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different.
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</p>
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<h5>
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<a name="math_toolkit.next_float.float_distance.h0"></a>
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<span class="phrase"><a name="math_toolkit.next_float.float_distance.synopsis"></a></span><a class="link" href="float_distance.html#math_toolkit.next_float.float_distance.synopsis">Synopsis</a>
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</h5>
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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">special_functions</span><span class="special">/</span><span class="identifier">next</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
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</pre>
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<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
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<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">FPT</span><span class="special">></span>
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<span class="identifier">FPT</span> <span class="identifier">float_distance</span><span class="special">(</span><span class="identifier">FPT</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">FPT</span> <span class="identifier">b</span><span class="special">);</span>
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<span class="special">}}</span> <span class="comment">// namespaces</span>
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</pre>
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<h5>
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<a name="math_toolkit.next_float.float_distance.h1"></a>
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<span class="phrase"><a name="math_toolkit.next_float.float_distance.description_float_distance"></a></span><a class="link" href="float_distance.html#math_toolkit.next_float.float_distance.description_float_distance">Description
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- float_distance</a>
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</h5>
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<p>
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Returns the distance between <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span>:
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the result is always a signed integer value (stored in floating-point type
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FPT) representing the number of distinct representations between <span class="emphasis"><em>a</em></span>
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and <span class="emphasis"><em>b</em></span>.
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</p>
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<p>
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Note that
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</p>
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">float_distance</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>
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always returns 0.
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</li>
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">float_distance</span><span class="special">(</span><span class="identifier">float_next</span><span class="special">(</span><span class="identifier">a</span><span class="special">),</span> <span class="identifier">a</span><span class="special">)</span></code>
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always returns -1.
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</li>
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<li class="listitem">
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<code class="computeroutput"><span class="identifier">float_distance</span><span class="special">(</span><span class="identifier">float_prior</span><span class="special">(</span><span class="identifier">a</span><span class="special">),</span> <span class="identifier">a</span><span class="special">)</span></code>
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always returns 1.
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</li>
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</ul></div>
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<p>
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The function <code class="computeroutput"><span class="identifier">float_distance</span></code>
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is equivalent to calculating the number of ULP (Units in the Last Place)
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between <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span> except that it
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returns a signed value indicating whether <code class="computeroutput"><span class="identifier">a</span>
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<span class="special">></span> <span class="identifier">b</span></code>
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or not.
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</p>
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<p>
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If the distance is too great then it may not be able to be represented as
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an exact integer by type FPT, but in practice this is unlikely to be a issue.
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</p>
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<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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