1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Calculating the Representation Distance Between Two floating-point Values (ULP) float_distance</title> 5<link rel="stylesheet" href="../../math.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../index.html" title="Math Toolkit 2.12.0"> 8<link rel="up" href="../next_float.html" title="Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values"> 9<link rel="prev" href="float_prior.html" title="Finding the Next Smaller Representable Value (float_prior)"> 10<link rel="next" href="float_advance.html" title="Advancing a floating-point Value by a Specific Representation Distance (ULP) float_advance"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> 15<td align="center"><a href="../../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="float_prior.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../next_float.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="float_advance.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 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 © 2006-2019 Nikhar 93 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 94 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 95 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 96 Daryle Walker and Xiaogang Zhang<p> 97 Distributed under the Boost Software License, Version 1.0. (See accompanying 98 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>) 99 </p> 100</div></td> 101</tr></table> 102<hr> 103<div class="spirit-nav"> 104<a accesskey="p" href="float_prior.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../next_float.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="float_advance.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 105</div> 106</body> 107</html> 108
