161 lines
12 KiB
HTML
161 lines
12 KiB
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<title>std::erfc, std::erfcf, std::erfcl</title>
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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>erfc, <span style="font-size:0.7em; line-height:130%">std::</span>erfcf, <span style="font-size:0.7em; line-height:130%">std::</span>erfcl</h1>
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<div id="contentSub"><span class="subpages">< <a href="cpp.html">cpp</a>‎ | <a href="cpp-numeric.html">numeric</a>‎ | <a href="cpp-numeric-math.html">math</a></span></div>
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<div>定义于头文件 <code><a href="cpp-header-cmath.html"><cmath></a></code></div>
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</td>
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<td></td>
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<td></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">float</span> erfc <span class="br0">(</span> <span class="kw4">float</span> arg <span class="br0">)</span><span class="sy4">;</span><br />
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<span class="kw4">float</span> erfcf<span class="br0">(</span> <span class="kw4">float</span> arg <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(1)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span> erfc <span class="br0">(</span> <span class="kw4">double</span> arg <span class="br0">)</span><span class="sy4">;</span></span></div>
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<td>(2)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span> erfc <span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> arg <span class="br0">)</span><span class="sy4">;</span><br />
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<span class="kw4">long</span> <span class="kw4">double</span> erfcl<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>
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<td>(3)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span> erfc <span class="br0">(</span> IntegralType arg <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(4)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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<tr class="t-dcl-sep">
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<td></td>
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<td></td>
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<td></td>
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<div class="t-li1"><span class="t-li">1-3)</span> 计算 <code>arg</code> 的<a href="https://en.wikipedia.org/wiki/Complementary_error_function" class="extiw" title="enwiki:Complementary error function">补误差函数</a>，即 <code>1.0-erf(arg)</code> ，但对于大的 <code>arg</code> 无精度损失。</div>
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<div class="t-li1"><span class="t-li">4)</span> 接受任何<a href="cpp-types-is_integral.html">整数类型</a>参数的重载集或函数模板。等价于 <span class="t-v">(2)</span> （参数被转型到 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> ）。</div>
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<h3><span class="mw-headline" id=".E5.8F.82.E6.95.B0">参数</span></h3>
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<table class="t-par-begin">
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<td>arg</td>
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<td>-</td>
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<td>浮点或<a href="cpp-types-is_integral.html">整数类型</a>值</td>
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</tr>
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</table>
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<h3><span class="mw-headline" id=".E8.BF.94.E5.9B.9E.E5.80.BC">返回值</span></h3>
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若不出现错误，则返回 <code>arg</code> 的补误差函数的值，即 <span class="mjax" style="display:none">\(\frac{2}{\sqrt{\pi} }\int_{arg}^{\infty}{e^{-{t^2} }\mathsf{d}t}\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;"><span class="t-mfrac"></span></span>
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<table>
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<td>2</td>
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</tr>
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<tr>
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<td><span class="t-mrad"><span>√</span><span>π</span></span></td>
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<span style="font-size: 1.3em; vertical-align:-0.08em; margin-right: 0.08em;">∫</span><span class="t-su t-su-b">∞<br />
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arg</span><i>e</i><sup>-t<span class="t-su">2<br /></span></sup>d<i>t</i> 或 <span class="mjax" style="display:none">\({\small 1-\operatorname{erf}(arg)}\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">1-erf(arg)</span> 。
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<p>若出现源于下溢的值域错误，则返回（舍入后的）正确结果。</p>
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<h3><span class="mw-headline" id=".E9.94.99.E8.AF.AF.E5.A4.84.E7.90.86">错误处理</span></h3>
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<p>报告 <span class="t-lc"><a href="cpp-numeric-math-math_errhandling.html">math_errhandling</a></span> 中指定的错误。</p>
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<p>若实现支持 IEEE 浮点算术（ IEC 60559 ），则</p>
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<ul>
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<li>若参数为 +∞ ，则返回 +0</li>
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<li>若参数为 -∞ ，则返回 2</li>
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<li>若参数为 NaN ，则返回 NaN</li>
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</ul>
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<h3><span class="mw-headline" id=".E6.B3.A8.E8.A7.A3">注解</span></h3>
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<p>对于 IEEE 兼容的 <code>double</code> 类型，若 <code>arg</code> > 26.55 则保证下溢。</p>
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<h3><span class="mw-headline" id=".E7.A4.BA.E4.BE.8B">示例</span></h3>
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<div class="t-example">
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<div class="t-example-live-link"></div>
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<div dir="ltr" class="mw-geshi" style="text-align: left;">
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<div class="cpp source-cpp">
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<pre class="de1"><span class="co2">#include <iostream></span>
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<span class="co2">#include <cmath></span>
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<span class="co2">#include <iomanip></span>
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<span class="kw4">double</span> normalCDF<span class="br0">(</span><span class="kw4">double</span> x<span class="br0">)</span> <span class="co1">// Phi(-∞, x) 又称为 N(x)</span>
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<span class="br0">{</span>
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<span class="kw1">return</span> std<span class="sy4">::</span><span class="me2">erfc</span><span class="br0">(</span><span class="sy2">-</span>x<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><span class="nu0">2</span><span class="sy4">;</span>
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<span class="br0">}</span>
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<span class="kw4">int</span> main<span class="br0">(</span><span class="br0">)</span>
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<span class="br0">{</span>
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<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"normal cumulative distribution function:<span class="es1">\n</span>"</span>
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<span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1783">std::<span class="me2">fixed</span></span></a> <span class="sy1"><<</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>
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<span class="kw1">for</span><span class="br0">(</span><span class="kw4">double</span> n<span class="sy1">=</span><span class="nu0">0</span><span class="sy4">;</span> n<span class="sy1"><</span><span class="nu0">1</span><span class="sy4">;</span> n<span class="sy2">+</span><span class="sy1">=</span><span class="nu16">0.1</span><span class="br0">)</span>
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<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"normalCDF("</span> <span class="sy1"><<</span> n <span class="sy1"><<</span> <span class="st0">") "</span> <span class="sy1"><<</span> <span class="nu0">100</span><span class="sy2">*</span>normalCDF<span class="br0">(</span>n<span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">"%<span class="es1">\n</span>"</span><span class="sy4">;</span>
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<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"special values:<span class="es1">\n</span>"</span>
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<span class="sy1"><<</span> <span class="st0">"erfc(-Inf) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">erfc</span><span class="br0">(</span><span class="sy2">-</span><a href="cpp-numeric-math-INFINITY.html"><span class="kw1376">INFINITY</span></a><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span>
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<span class="sy1"><<</span> <span class="st0">"erfc(Inf) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">erfc</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"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
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<span class="br0">}</span></pre></div>
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</div>
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<p>输出：</p>
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<div dir="ltr" class="mw-geshi" style="text-align: left;">
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<div class="text source-text">
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<pre class="de1">normal cumulative distribution function:
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normalCDF(0.00) 50.00%
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normalCDF(0.10) 53.98%
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normalCDF(0.20) 57.93%
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normalCDF(0.30) 61.79%
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normalCDF(0.40) 65.54%
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normalCDF(0.50) 69.15%
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normalCDF(0.60) 72.57%
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normalCDF(0.70) 75.80%
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normalCDF(0.80) 78.81%
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normalCDF(0.90) 81.59%
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normalCDF(1.00) 84.13%
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special values:
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erfc(-Inf) = 2.00
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erfc(Inf) = 0.00</pre></div>
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</div>
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</div>
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<h3><span class="mw-headline" id=".E5.8F.82.E9.98.85">参阅</span></h3>
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<table class="t-dsc-begin">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-math-erf.html"><span class="t-lines"><span>erf</span><span>erff</span><span>erfl</span></span></a></div>
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<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>
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</div>
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</td>
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<td>误差函数<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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</table>
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<h3><span class="mw-headline" id=".E5.A4.96.E9.83.A8.E9.93.BE.E6.8E.A5">外部链接</span></h3>
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<p><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Erfc.html">Weisstein, Eric W. "Erfc."</a> 来自 MathWorld--A Wolfram Web Resource 。</p>
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</div>
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<div class="visualClear"></div>
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</div>
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