klarkxy/hustoj
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity
Files
master
hustoj/web/cppreference-zh/chmhelp/cpp-numeric-math-erf.html
klarkxy 196e706fe4 上传cppreference
2025-08-01 12:57:54 +08:00

178 lines
14 KiB
HTML
Raw Permalink Blame History

<!DOCTYPE html>
<html lang="zh" dir="ltr" class="client-nojs" xmlns="http://www.w3.org/1999/xhtml" xml:lang="zh">
<head><meta http-equiv="x-ua-compatible" content="ie=edge">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>std::erf, std::erff, std::erfl</title>
<link rel="stylesheet" href="ext.css" />
<link rel="stylesheet" href="site_modules.css" />
</head>
<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-cpp_numeric_math_erf skin-cppreference2 action-view cpp-navbar">
<div id="cpp-content-base">
<div id="content"><a id="top"></a>
<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>erf, <span style="font-size:0.7em; line-height:130%">std::</span>erff, <span style="font-size:0.7em; line-height:130%">std::</span>erfl</h1>
<div id="bodyContent">
<div id="contentSub"><span class="subpages">&lt; <a href="cpp.html">cpp</a>&lrm; | <a href="cpp-numeric.html">numeric</a>&lrm; | <a href="cpp-numeric-math.html">math</a></span></div>
<div id="mw-content-text" lang="zh" dir="ltr" class="mw-content-ltr" xml:lang="zh">
<table class="t-dcl-begin">
<tbody>
<tr class="t-dsc-header">
<td>
<div>&#23450;&#20041;&#20110;&#22836;&#25991;&#20214; <code><a href="cpp-header-cmath.html">&lt;cmath&gt;</a></code></div>
</td>
<td></td>
<td></td>
</tr>
<tr class="t-dcl t-since-cxx11">
<td>
<div><span class="mw-geshi cpp source-cpp"><span class="kw4">float</span> &nbsp; &nbsp; &nbsp; erf <span class="br0">(</span> <span class="kw4">float</span> arg <span class="br0">)</span><span class="sy4">;</span><br />
<span class="kw4">float</span> &nbsp; &nbsp; &nbsp; erff<span class="br0">(</span> <span class="kw4">float</span> arg <span class="br0">)</span><span class="sy4">;</span></span></div>
</td>
<td>(1)</td>
<td><span class="t-mark-rev t-since-cxx11">(C++11 &#36215;)</span></td>
</tr>
<tr class="t-dcl t-since-cxx11">
<td>
<div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span> &nbsp; &nbsp; &nbsp;erf <span class="br0">(</span> <span class="kw4">double</span> arg <span class="br0">)</span><span class="sy4">;</span></span></div>
</td>
<td>(2)</td>
<td><span class="t-mark-rev t-since-cxx11">(C++11 &#36215;)</span></td>
</tr>
<tr class="t-dcl t-since-cxx11">
<td>
<div><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span> erf <span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> arg <span class="br0">)</span><span class="sy4">;</span><br />
<span class="kw4">long</span> <span class="kw4">double</span> erfl<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> arg <span class="br0">)</span><span class="sy4">;</span></span></div>
</td>
<td>(3)</td>
<td><span class="t-mark-rev t-since-cxx11">(C++11 &#36215;)</span></td>
</tr>
<tr class="t-dcl t-since-cxx11">
<td>
<div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span> &nbsp; &nbsp; &nbsp;erf <span class="br0">(</span> IntegralType arg <span class="br0">)</span><span class="sy4">;</span></span></div>
</td>
<td>(4)</td>
<td><span class="t-mark-rev t-since-cxx11">(C++11 &#36215;)</span></td>
</tr>
<tr class="t-dcl-sep">
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<div class="t-li1"><span class="t-li">1-3)</span> &#35745;&#31639; <code>arg</code> &#30340;<a href="https://en.wikipedia.org/wiki/Error_function" class="extiw" title="enwiki:Error function">&#35823;&#24046;&#20989;&#25968;</a>&#12290;</div>
<div class="t-li1"><span class="t-li">4)</span> &#25509;&#21463;&#20219;&#20309;<a href="cpp-types-is_integral.html">&#25972;&#25968;&#31867;&#22411;</a>&#21442;&#25968;&#30340;&#37325;&#36733;&#38598;&#25110;&#20989;&#25968;&#27169;&#26495;&#65292;&#31561;&#20215;&#20110; <span class="t-v">(2)</span> &#65288;&#21442;&#25968;&#34987;&#36716;&#22411;&#21040; <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> &#65289;&#12290;</div>
<h3><span class="mw-headline" id=".E5.8F.82.E6.95.B0">&#21442;&#25968;</span></h3>
<table class="t-par-begin">
<tr class="t-par">
<td>arg</td>
<td>-</td>
<td>&#28014;&#28857;&#25110;<a href="cpp-types-is_integral.html">&#25972;&#25968;&#31867;&#22411;</a>&#20540;</td>
</tr>
</table>
<h3><span class="mw-headline" id=".E8.BF.94.E5.9B.9E.E5.80.BC">&#36820;&#22238;&#20540;</span></h3>
&#33509;&#19981;&#20986;&#29616;&#38169;&#35823;&#65292;&#21017;&#36820;&#22238; <code>arg</code> &#30340;&#35823;&#24046;&#20989;&#25968;&#30340;&#20540;&#65292;&#21363; <span class="mjax" style="display:none">\(\frac{2}{\sqrt{\pi} }\int_{0}^{arg}{e^{-{t^2} }\mathsf{d}t}\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;"><span class="t-mfrac"></span></span>
<table>
<tr>
<td>2</td>
</tr>
<tr>
<td><span class="t-mrad"><span>&radic;</span><span>&pi;</span></span></td>
</tr>
</table>
<span style="font-size: 1.3em; vertical-align:-0.08em; margin-right: 0.08em;">&int;</span><span class="t-su t-su-b">arg<br />
0</span><i>e</i><sup>-t<span class="t-su">2<br /></span></sup>d<i>t</i> &#12290; &#33509;&#22240;&#19979;&#28322;&#20986;&#29616;&#20540;&#22495;&#38169;&#35823;&#65292;&#21017;&#36820;&#22238;&#65288;&#33293;&#20837;&#21518;&#30340;&#65289;&#27491;&#30830;&#32467;&#26524;&#65292;&#21363; <span class="mjax" style="display:none">\(\frac{2\cdot arg}{\sqrt{\pi} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;"><span class="t-mfrac"></span></span>
<table>
<tr>
<td>2*arg</td>
</tr>
<tr>
<td><span class="t-mrad"><span>&radic;</span><span>&pi;</span></span></td>
</tr>
</table>
&#12290;
<h3><span class="mw-headline" id=".E9.94.99.E8.AF.AF.E5.A4.84.E7.90.86">&#38169;&#35823;&#22788;&#29702;</span></h3>
<p>&#25253;&#21578; <span class="t-lc"><a href="cpp-numeric-math-math_errhandling.html">math_errhandling</a></span> &#20013;&#25351;&#23450;&#30340;&#38169;&#35823;&#12290;</p>
<p>&#33509;&#23454;&#29616;&#25903;&#25345; IEEE &#28014;&#28857;&#31639;&#26415;&#65288; IEC 60559 &#65289;&#65292;&#21017;</p>
<ul>
<li>&#33509;&#21442;&#25968;&#20026; &plusmn;0 &#65292;&#21017;&#36820;&#22238; &plusmn;0</li>
<li>&#33509;&#21442;&#25968;&#20026; &plusmn;&infin; &#65292;&#21017;&#36820;&#22238; &plusmn;1</li>
<li>&#33509;&#21442;&#25968;&#20026; NaN &#65292;&#21017;&#36820;&#22238; NaN</li>
</ul>
<h3><span class="mw-headline" id=".E6.B3.A8.E8.A7.A3">&#27880;&#35299;</span></h3>
<p>&#33509; <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="sy3">|</span>arg<span class="sy3">|</span> <span class="sy1">&lt;</span> <a href="cpp-types-climits.html"><span class="kw412">DBL_MIN</span></a><span class="sy2">*</span><span class="br0">(</span>sqrt<span class="br0">(</span>&pi;<span class="br0">)</span><span class="sy2">/</span><span class="nu0">2</span><span class="br0">)</span></span></span> &#21017;&#20445;&#35777;&#19979;&#28322;&#12290;</p>
<span class="mjax" style="display:none">\(\operatorname{erf}(\frac{x}{\sigma \sqrt{2} })\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">erf(<span class="t-mfrac"></span></span>
<table>
<tr>
<td>x</td>
</tr>
<tr>
<td>&sigma;<span class="t-mrad"><span>&radic;</span><span>2</span></span></td>
</tr>
</table>
) &#26159;&#27979;&#37327;&#32467;&#26524;&#23567;&#20110;&#19982;&#24179;&#22343;&#25968;&#30456;&#24046; <span class="mjax" style="display:none">\(x\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">x</span> &#30340;&#20540;&#30340;&#27010;&#29575;&#65292;&#20854;&#35823;&#24046;&#26381;&#20174;&#26631;&#20934;&#24046;&#20026; <span class="mjax" style="display:none">\(\sigma\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">&sigma;</span> &#30340;&#27491;&#24577;&#20998;&#24067;&#12290;
<h3><span class="mw-headline" id=".E7.A4.BA.E4.BE.8B">&#31034;&#20363;</span></h3>
<div class="t-example">
<p>&#20197;&#19979;&#31034;&#20363;&#35745;&#31639;&#27491;&#24577;&#20998;&#24067;&#38543;&#26426;&#21464;&#37327;&#22312;&#21306;&#38388; (x1, x2) &#19978;&#30340;&#27010;&#29575;</p>
<div class="t-example-live-link"></div>
<div dir="ltr" class="mw-geshi" style="text-align: left;">
<div class="cpp source-cpp">
<pre class="de1"><span class="co2">#include &lt;iostream&gt;</span>
<span class="co2">#include &lt;cmath&gt;</span>
<span class="co2">#include &lt;iomanip&gt;</span>
<span class="kw4">double</span> phi<span class="br0">(</span><span class="kw4">double</span> x1, <span class="kw4">double</span> x2<span class="br0">)</span>
<span class="br0">{</span>
<span class="kw1">return</span> <span class="br0">(</span>std<span class="sy4">::</span><span class="me2">erf</span><span class="br0">(</span>x2<span class="sy2">/</span><a href="cpp-numeric-math-sqrt.html"><span class="kw1329">std::<span class="me2">sqrt</span></span></a><span class="br0">(</span><span class="nu0">2</span><span class="br0">)</span><span class="br0">)</span> <span class="sy2">-</span> std<span class="sy4">::</span><span class="me2">erf</span><span class="br0">(</span>x1<span class="sy2">/</span><a href="cpp-numeric-math-sqrt.html"><span class="kw1329">std::<span class="me2">sqrt</span></span></a><span class="br0">(</span><span class="nu0">2</span><span class="br0">)</span><span class="br0">)</span><span class="br0">)</span><span class="sy2">/</span><span class="nu0">2</span><span class="sy4">;</span>
<span class="br0">}</span>
<span class="kw4">int</span> main<span class="br0">(</span><span class="br0">)</span>
<span class="br0">{</span>
<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1">&lt;&lt;</span> <span class="st0">&quot;normal variate probabilities:<span class="es1">\n</span>&quot;</span>
<span class="sy1">&lt;&lt;</span> <a href="cpp-io-manip-fixed.html"><span class="kw1783">std::<span class="me2">fixed</span></span></a> <span class="sy1">&lt;&lt;</span> <a href="cpp-io-manip-setprecision.html"><span class="kw1795">std::<span class="me2">setprecision</span></span></a><span class="br0">(</span><span class="nu0">2</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">for</span><span class="br0">(</span><span class="kw4">int</span> n<span class="sy1">=</span><span class="sy2">-</span><span class="nu0">4</span><span class="sy4">;</span> n<span class="sy1">&lt;</span><span class="nu0">4</span><span class="sy4">;</span> <span class="sy2">++</span>n<span class="br0">)</span>
<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1">&lt;&lt;</span> <span class="st0">&quot;[&quot;</span> <span class="sy1">&lt;&lt;</span> <a href="cpp-io-manip-setw.html"><span class="kw1796">std::<span class="me2">setw</span></span></a><span class="br0">(</span><span class="nu0">2</span><span class="br0">)</span> <span class="sy1">&lt;&lt;</span> n <span class="sy1">&lt;&lt;</span> <span class="st0">&quot;:&quot;</span> <span class="sy1">&lt;&lt;</span> <a href="cpp-io-manip-setw.html"><span class="kw1796">std::<span class="me2">setw</span></span></a><span class="br0">(</span><span class="nu0">2</span><span class="br0">)</span> <span class="sy1">&lt;&lt;</span> n<span class="sy2">+</span><span class="nu0">1</span> <span class="sy1">&lt;&lt;</span> <span class="st0">&quot;]: &quot;</span>
<span class="sy1">&lt;&lt;</span> <a href="cpp-io-manip-setw.html"><span class="kw1796">std::<span class="me2">setw</span></span></a><span class="br0">(</span><span class="nu0">5</span><span class="br0">)</span> <span class="sy1">&lt;&lt;</span> <span class="nu0">100</span><span class="sy2">*</span>phi<span class="br0">(</span>n, n<span class="sy2">+</span><span class="nu0">1</span><span class="br0">)</span> <span class="sy1">&lt;&lt;</span> <span class="st0">&quot;%<span class="es1">\n</span>&quot;</span><span class="sy4">;</span>
<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1">&lt;&lt;</span> <span class="st0">&quot;special values:<span class="es1">\n</span>&quot;</span>
<span class="sy1">&lt;&lt;</span> <span class="st0">&quot;erf(-0) = &quot;</span> <span class="sy1">&lt;&lt;</span> std<span class="sy4">::</span><span class="me2">erf</span><span class="br0">(</span><span class="sy2">-</span><span class="nu16">0.0</span><span class="br0">)</span> <span class="sy1">&lt;&lt;</span> <span class="st0">&#39;<span class="es1">\n</span>&#39;</span>
<span class="sy1">&lt;&lt;</span> <span class="st0">&quot;erf(Inf) = &quot;</span> <span class="sy1">&lt;&lt;</span> std<span class="sy4">::</span><span class="me2">erf</span><span class="br0">(</span><a href="cpp-numeric-math-INFINITY.html"><span class="kw1376">INFINITY</span></a><span class="br0">)</span> <span class="sy1">&lt;&lt;</span> <span class="st0">&#39;<span class="es1">\n</span>&#39;</span><span class="sy4">;</span>
<span class="br0">}</span></pre></div>
</div>
<p>&#36755;&#20986;&#65306;</p>
<div dir="ltr" class="mw-geshi" style="text-align: left;">
<div class="text source-text">
<pre class="de1">normal variate probabilities:
[-4:-3]: 0.13%
[-3:-2]: 2.14%
[-2:-1]: 13.59%
[-1: 0]: 34.13%
[ 0: 1]: 34.13%
[ 1: 2]: 13.59%
[ 2: 3]: 2.14%
[ 3: 4]: 0.13%
special values:
erf(-0) = -0.00
erf(Inf) = 1.00</pre></div>
</div>
</div>
<h3><span class="mw-headline" id=".E5.8F.82.E9.98.85">&#21442;&#38405;</span></h3>
<table class="t-dsc-begin">
<tr class="t-dsc">
<td>
<div class="t-dsc-member-div">
<div><a href="cpp-numeric-math-erfc.html"><span class="t-lines"><span>erfc</span><span>erfcf</span><span>erfcl</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>&#34917;&#35823;&#24046;&#20989;&#25968;<br />
<span class="t-mark">(&#20989;&#25968;)</span></td>
</tr>
</table>
<h3><span class="mw-headline" id=".E5.A4.96.E9.83.A8.E9.93.BE.E6.8E.A5">&#22806;&#37096;&#38142;&#25509;</span></h3>
<p><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Erf.html">Weisstein, Eric W. &quot;Erf.&quot;</a> &#26469;&#33258; MathWorld--A Wolfram Web Resource &#12290;</p>
</div>
<div class="visualClear"></div>
</div>
</div>
</div>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink