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<!DOCTYPE HTML PUBLIC "-//W3O//DTD W3 HTML 2.0//EN"><!-- This collection of hypertext pages is Copyright 1995-2005 by Steve Summit. --><!-- Content from the book "C Programming FAQs: Frequently Asked Questions" --><!-- (Addison-Wesley, 1995, ISBN 0-201-84519-9) is made available here by --><!-- permission of the author and the publisher as a service to the community. --><!-- It is intended to complement the use of the published text --><!-- and is protected by international copyright laws. --><!-- The on-line content may be accessed freely for personal use --><!-- but may not be published or retransmitted without explicit permission. --><!-- --><!-- this page built Sat Dec 24 21:47:46 2005 by faqproc version 2.7 --><!-- from source file fp.sgml dated Fri Jul 2 23:51:18 2004 --><!-- corresponding to FAQ list version 4.0 --><html><!-- Mirrored from c-faq.com/fp/fpequal.html by HTTrack Website Copier/3.x [XR&CO'2008], Sat, 14 Mar 2009 07:59:00 GMT --><head><meta name=GENERATOR content="faqproc"><title>Question 14.5</title><link href="degrees.html" rev=precedes><link href="round.html" rel=precedes><link href="index.html" rev=subdocument></head><body bgcolor="#ffffff"><a href="degrees.html" rev=precedes><img src="../images/buttonleft.gif" alt="prev"></a><a href="index.html" rev=subdocument><img src="../images/buttonup.gif" alt="up"></a><a href="round.html" rel=precedes><img src="../images/buttonright.gif" alt="next"></a> <a href="../index-2.html"><img src="../images/buttontop.gif" alt="top/contents"></a><a href="../search.html"><img src="../images/buttonsrch.gif" alt="search"></a><hr><p><!-- qbegin --><h1>comp.lang.c FAQ list<font color=blue>·</font><!-- qtag -->Question 14.5</h1><p><font face=Helvetica size=8 color=blue><b>Q:</b></font>What's a good way to check for ``close enough''floating-point equality?</p><p><hr><p><font face=Helvetica size=8 color=blue><b>A:</b></font>Since the absolute accuracy of floating point values varies,by definition,with their magnitude,thebest wayof comparing two floating point valuesis to use an accuracy thresholdwhich is relativeto the magnitude of the numbers being compared.Rather than<pre> double a, b; ... if(a == b) /* WRONG */</pre>use something like<pre> #include <math.h> if(fabs(a - b) <= epsilon * fabs(a))</pre>where<TT>epsilon</TT>is a value chosen to set thedegree of ``closeness''(and where you know that <TT>a</TT> will not be zero).The precise value of <TT>epsilon</TT> may still have to be chosen withcare:its appropriate value may be quite small and related only to themachine's floating-pointprecision,orit may be largerif the numbers being comparedare inherently less accurateor are the results ofa chain of calculationswhichcompoundsaccuracy lossesover several steps.(Also,you may have to make the thresholda function of <TT>b</TT>,or of both <TT>a</TT> and <TT>b</TT>.)</p><p>A decidedly inferior approach,not generally recommended,would be to use an absolute threshold:<pre> if(fabs(a - b) < 0.001) /* POOR */</pre>Absolute``fuzz factors''like0.001never seem to workfor very long,however.As the numbersbeing comparedchange,it's likely that twosmallnumbersthat should be taken as differenthappen to be within 0.001 of each other,or that two large numbers,which should have been treated as equal,differ by more than 0.001 .(And,of course,the problems merely shift around,and do not go away,when the fuzz factor is tweaked to 0.005,or 0.0001,or any other absolute number.)</p><p>Doug Gwyn suggestsusingthefollowing``relative difference''function.Itreturns the relative difference of two real numbers:0.0 if they are exactly the same,otherwise the ratio of the difference to the larger of the two.<pre>#define Abs(x) ((x) < 0 ? -(x) : (x))#define Max(a, b) ((a) > (b) ? (a) : (b))double RelDif(double a, double b){ double c = Abs(a); double d = Abs(b); d = Max(c, d); return d == 0.0 ? 0.0 : Abs(a - b) / d;}</pre>Typical usage is<pre> if(RelDif(a, b) <= TOLERANCE) ...</pre></p><p>References:Knuth Sec. 4.2.2 pp. 217-8<br></p><!-- aend --><p><hr><a href="degrees.html" rev=precedes><img src="../images/buttonleft.gif" alt="prev"></a><a href="index.html" rev=subdocument><img src="../images/buttonup.gif" alt="up"></a><a href="round.html" rel=precedes><img src="../images/buttonright.gif" alt="next"></a> <a href="../questions.html"><img src="../images/buttontop.gif" alt="contents"></a><a href="../search.html"><img src="../images/buttonsrch.gif" alt="search"></a><br><!-- lastfooter --><a href="../about.html">about this FAQ list</a> <a href="../eskimo.html">about eskimo</a> <a href="../search.html">search</a> <a href="../feedback.html">feedback</a> <a href="copyright.html">copyright</a><p>Hosted by<a href="http://www.eskimo.com/"><img src="../../www.eskimo.com/img/link/eskitiny.gif" alt="Eskimo North"></a></body><!-- Mirrored from c-faq.com/fp/fpequal.html by HTTrack Website Copier/3.x [XR&CO'2008], Sat, 14 Mar 2009 07:59:00 GMT --></html>⌨️ 快捷键说明
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