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| 4 | <title>Calculating the Representation Distance Between Two floating-point Values (ULP) float_distance</title> | |
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| 24 | </div> | |
| 25 | <div class="section"> | |
| 26 | <div class="titlepage"><div><div><h3 class="title"> | |
| 27 | <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 | |
| 28 | Representation Distance Between Two floating-point Values (ULP) float_distance</a> | |
| 29 | </h3></div></div></div> | |
| 30 | <p> | |
| 31 | Function float_distance finds the number of gaps/bits/ULP between any two | |
| 32 | floating-point values. If the significands of floating-point numbers are | |
| 33 | viewed as integers, then their difference is the number of ULP/gaps/bits | |
| 34 | different. | |
| 35 | </p> | |
| 36 | <h5> | |
| 37 | <a name="math_toolkit.next_float.float_distance.h0"></a> | |
| 38 | <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> | |
| 39 | </h5> | |
| 40 | <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> | |
| 41 | </pre> | |
| 42 | <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> | |
| 43 | ||
| 44 | <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">FPT</span><span class="special">></span> | |
| 45 | <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> | |
| 46 | ||
| 47 | <span class="special">}}</span> <span class="comment">// namespaces</span> | |
| 48 | </pre> | |
| 49 | <h5> | |
| 50 | <a name="math_toolkit.next_float.float_distance.h1"></a> | |
| 51 | <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 | |
| 52 | - float_distance</a> | |
| 53 | </h5> | |
| 54 | <p> | |
| 55 | Returns the distance between <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span>: | |
| 56 | the result is always a signed integer value (stored in floating-point type | |
| 57 | FPT) representing the number of distinct representations between <span class="emphasis"><em>a</em></span> | |
| 58 | and <span class="emphasis"><em>b</em></span>. | |
| 59 | </p> | |
| 60 | <p> | |
| 61 | Note that | |
| 62 | </p> | |
| 63 | <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> | |
| 64 | <li class="listitem"> | |
| 65 | <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> | |
| 66 | always returns 0. | |
| 67 | </li> | |
| 68 | <li class="listitem"> | |
| 69 | <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> | |
| 70 | always returns -1. | |
| 71 | </li> | |
| 72 | <li class="listitem"> | |
| 73 | <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> | |
| 74 | always returns 1. | |
| 75 | </li> | |
| 76 | </ul></div> | |
| 77 | <p> | |
| 78 | The function <code class="computeroutput"><span class="identifier">float_distance</span></code> | |
| 79 | is equivalent to calculating the number of ULP (Units in the Last Place) | |
| 80 | between <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span> except that it | |
| 81 | returns a signed value indicating whether <code class="computeroutput"><span class="identifier">a</span> | |
| 82 | <span class="special">></span> <span class="identifier">b</span></code> | |
| 83 | or not. | |
| 84 | </p> | |
| 85 | <p> | |
| 86 | If the distance is too great then it may not be able to be represented as | |
| 87 | an exact integer by type FPT, but in practice this is unlikely to be a issue. | |
| 88 | </p> | |
| 89 | </div> | |
| 90 | <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> | |
| 91 | <td align="left"></td> | |
| 92 | <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, | |
| 93 | Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert | |
| 94 | Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani, | |
| 95 | Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> | |
| 96 | Distributed under the Boost Software License, Version 1.0. (See accompanying | |
| 97 | 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>) | |
| 98 | </p> | |
| 99 | </div></td> | |
| 100 | </tr></table> | |
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| 104 | </div> | |
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