1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Tolerance-based comparisons</title> 5<link rel="stylesheet" href="../../../../boostbook.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../../../index.html" title="Boost.Test"> 8<link rel="up" href="../floating_point.html" title="Floating point comparison"> 9<link rel="prev" href="customizing_for_tolerance.html" title="Enabling tolerance for user-defined types"> 10<link rel="next" href="floating_points_comparison_theory.html" title="Theory behind floating point comparisons"> 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="customizing_for_tolerance.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floating_point.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="floating_points_comparison_theory.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h5 class="title"> 27<a name="boost_test.testing_tools.extended_comparison.floating_point.floating_points_comparison_impl"></a><a class="link" href="floating_points_comparison_impl.html" title="Tolerance-based comparisons">Tolerance-based 28 comparisons</a> 29</h5></div></div></div> 30<p> 31 Assertions in the <span class="emphasis"><em>Unit Test Framework</em></span> use two kinds 32 of comparison. For <code class="computeroutput"><span class="identifier">u</span></code> 33 being close to zero with absolute tolerance <code class="computeroutput"><span class="identifier">eps</span></code>: 34 </p> 35<pre class="programlisting"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">u</span><span class="special">)</span> <span class="special"><=</span> <span class="identifier">eps</span><span class="special">;</span> <span class="comment">// (abs)</span> 36</pre> 37<p> 38 For <code class="computeroutput"><span class="identifier">u</span></code> and <code class="computeroutput"><span class="identifier">v</span></code> being close with relative tolerance 39 <code class="computeroutput"><span class="identifier">eps</span></code>: 40 </p> 41<pre class="programlisting"> <span class="identifier">abs</span><span class="special">(</span><span class="identifier">u</span> <span class="special">-</span> <span class="identifier">v</span><span class="special">)/</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">u</span><span class="special">)</span> <span class="special"><=</span> <span class="identifier">eps</span> 42<span class="special">&&</span> <span class="identifier">abs</span><span class="special">(</span><span class="identifier">u</span> <span class="special">-</span> <span class="identifier">v</span><span class="special">)/</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">v</span><span class="special">)</span> <span class="special"><=</span> <span class="identifier">eps</span><span class="special">;</span> <span class="comment">// (rel)</span> 43</pre> 44<p> 45 For rationale for choosing these formulae, see section <a class="link" href="floating_points_comparison_theory.html" title="Theory behind floating point comparisons">Floating 46 point comparison algorithms</a>. 47 </p> 48<p> 49 Assertion <a class="link" href="../../../utf_reference/testing_tool_ref/assertion_boost_test_universal_macro.html" title="BOOST_TEST"><code class="computeroutput"><span class="identifier">BOOST_TEST</span></code></a> (when comparing floating-point 50 numbers) uses the following algorithm: 51 </p> 52<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 53<li class="listitem"> 54 When either value <code class="computeroutput"><span class="identifier">u</span></code> 55 or <code class="computeroutput"><span class="identifier">v</span></code> is zero, evaluates 56 formula (abs) on the other value. 57 </li> 58<li class="listitem"> 59 When the specified tolerance is zero, performs direct (native) comparison 60 between <code class="computeroutput"><span class="identifier">u</span></code> and <code class="computeroutput"><span class="identifier">v</span></code>. 61 </li> 62<li class="listitem"> 63 Otherwise, performs formula (rel) on <code class="computeroutput"><span class="identifier">u</span></code> 64 and <code class="computeroutput"><span class="identifier">v</span></code>. 65 </li> 66</ul></div> 67<div class="note"><table border="0" summary="Note"> 68<tr> 69<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../doc/src/images/note.png"></td> 70<th align="left">Note</th> 71</tr> 72<tr><td align="left" valign="top"> 73<p> 74 Therefore in order to check if a number is close to zero with tolerance, 75 you need to type: 76 </p> 77<pre class="programlisting"><span class="identifier">BOOST_TEST</span><span class="special">(</span><span class="identifier">v</span> <span class="special">==</span> <span class="identifier">T</span><span class="special">(</span><span class="number">0</span><span class="special">),</span> <span class="identifier">tt</span><span class="special">::</span><span class="identifier">tolerance</span><span class="special">(</span><span class="identifier">eps</span><span class="special">));</span> 78</pre> 79</td></tr> 80</table></div> 81<p> 82 The compatibility assertions <a class="link" href="../../../utf_reference/testing_tool_ref/assertion_boost_level_close.html" title="BOOST_<level>_CLOSE"><code class="computeroutput"><span class="identifier">BOOST_</span><span class="special"><</span><span class="identifier">level</span><span class="special">></span><span class="identifier">_CLOSE</span></code></a> and <a class="link" href="../../../utf_reference/testing_tool_ref/assertion_boost_level_close_fraction.html" title="BOOST_<level>_CLOSE_FRACTION"><code class="computeroutput"><span class="identifier">BOOST_</span><span class="special"><</span><span class="identifier">level</span><span class="special">></span><span class="identifier">_CLOSE_FRACTION</span></code></a> perform formula 83 (rel). 84 </p> 85<p> 86 The compatibility assertion <a class="link" href="../../../utf_reference/testing_tool_ref/assertion_boost_level_small.html" title="BOOST_<level>_SMALL"><code class="computeroutput"><span class="identifier">BOOST_</span><span class="special"><</span><span class="identifier">level</span><span class="special">></span><span class="identifier">_SMALL</span></code></a> performs formula (abs). 87 </p> 88<p> 89 The <span class="emphasis"><em>Unit Test Framework</em></span> also provides unary predicate 90 <code class="computeroutput"><a class="link" href="../../../../boost/math/fpc/small_with_tolerance.html" title="Class template small_with_tolerance">small_with_tolerance</a></code> and 91 binary predicate predicate <code class="computeroutput"><a class="link" href="../../../../boost/math/fpc/close_at_tolerance.html" title="Class template close_at_tolerance">close_at_tolerance</a></code> that 92 implement formula (abs) and (rel) respectively. 93 </p> 94<h4> 95<a name="boost_test.testing_tools.extended_comparison.floating_point.floating_points_comparison_impl.h0"></a> 96 <span class="phrase"><a name="boost_test.testing_tools.extended_comparison.floating_point.floating_points_comparison_impl.tolerance_in_operator"></a></span><a class="link" href="floating_points_comparison_impl.html#boost_test.testing_tools.extended_comparison.floating_point.floating_points_comparison_impl.tolerance_in_operator">Tolerance 97 in <code class="computeroutput"><span class="keyword">operator</span><span class="special"><</span></code></a> 98 </h4> 99<p> 100 Tolerance-based computations also apply to <code class="computeroutput"><span class="keyword">operator</span><span class="special"><</span></code> and other relational operators. The 101 semantics are defined as follows: 102 </p> 103<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 104<li class="listitem"> 105 <span class="emphasis"><em>less-at-tolerance</em></span> <==> <span class="emphasis"><em>strictly-less</em></span> 106 and not <span class="emphasis"><em>close-at-tolerance</em></span> 107 </li> 108<li class="listitem"> 109 <span class="emphasis"><em>greater-at-tolerance</em></span> <==> <span class="emphasis"><em>strictly-greater</em></span> 110 and not <span class="emphasis"><em>close-at-tolerance</em></span> 111 </li> 112<li class="listitem"> 113 <span class="emphasis"><em>less-or-equal-at-tolerance</em></span> <==> <span class="emphasis"><em>strictly-less</em></span> 114 or <span class="emphasis"><em>close-at-tolerance</em></span> 115 </li> 116<li class="listitem"> 117 <span class="emphasis"><em>greater-or-equal-at-tolerance</em></span> <==> <span class="emphasis"><em>strictly-greater</em></span> 118 or <span class="emphasis"><em>close-at-tolerance</em></span> 119 </li> 120</ul></div> 121<div class="note"><table border="0" summary="Note"> 122<tr> 123<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../doc/src/images/note.png"></td> 124<th align="left">Note</th> 125</tr> 126<tr><td align="left" valign="top"><p> 127 This implies that the exactly one of these: <code class="computeroutput"><span class="identifier">u</span> 128 <span class="special"><</span> <span class="identifier">v</span></code>, 129 <code class="computeroutput"><span class="identifier">u</span> <span class="special">==</span> 130 <span class="identifier">v</span></code>, <code class="computeroutput"><span class="identifier">u</span> 131 <span class="special">></span> <span class="identifier">v</span></code>, 132 passes with <a class="link" href="../../../utf_reference/testing_tool_ref/assertion_boost_test_universal_macro.html" title="BOOST_TEST"><code class="computeroutput"><span class="identifier">BOOST_TEST</span></code></a> at any given tolerance. 133 </p></td></tr> 134</table></div> 135<div class="caution"><table border="0" summary="Caution"> 136<tr> 137<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../../doc/src/images/caution.png"></td> 138<th align="left">Caution</th> 139</tr> 140<tr><td align="left" valign="top"><p> 141 Relation <span class="emphasis"><em>less-at-tolerance</em></span> is not a <span class="emphasis"><em>Strict 142 Weak Ordering</em></span> as it lacks the <span class="emphasis"><em>transitivity of 143 the equivalence</em></span>; using it as predicate in <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">map</span></code> or any order-based STL algorithm 144 would result in undefined behavior. 145 </p></td></tr> 146</table></div> 147</div> 148<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 149<td align="left"></td> 150<td align="right"><div class="copyright-footer">Copyright © 2001-2020 Boost.Test contributors<p> 151 Distributed under the Boost Software License, Version 1.0. (See accompanying 152 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>) 153 </p> 154</div></td> 155</tr></table> 156<hr> 157<div class="spirit-nav"> 158<a accesskey="p" href="customizing_for_tolerance.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floating_point.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="floating_points_comparison_theory.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> 159</div> 160</body> 161</html> 162
