218 lines
16 KiB
HTML
218 lines
16 KiB
HTML
<!DOCTYPE html>
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<html lang="zh" dir="ltr" class="client-nojs" xmlns="http://www.w3.org/1999/xhtml" xml:lang="zh">
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<title>std::sqrt, std::sqrtf, std::sqrtl</title>
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<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-cpp_numeric_math_sqrt skin-cppreference2 action-view cpp-navbar">
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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>sqrt, <span style="font-size:0.7em; line-height:130%">std::</span>sqrtf, <span style="font-size:0.7em; line-height:130%">std::</span>sqrtl</h1>
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<div id="bodyContent">
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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 id="mw-content-text" lang="zh" dir="ltr" class="mw-content-ltr" xml:lang="zh">
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<table class="t-dcl-begin">
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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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<td></td>
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<td rowspan="142">(1)</td>
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<td></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">float</span> sqrt <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 class="t-dcl-nopad"></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">float</span> sqrtf<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 class="t-dcl-nopad"></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> sqrt <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 class="t-dcl-nopad"></td>
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<td rowspan="142">(3)</td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span> sqrt <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 class="t-dcl-nopad"></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span> sqrtl<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>
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<td class="t-dcl-nopad"></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> sqrt <span class="br0">(</span> IntegralType arg <span class="br0">)</span><span class="sy4">;</span></span></div>
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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>
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<tr class="t-dcl-sep">
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<div class="t-li1"><span class="t-li">1-3)</span> 计算 <code>arg</code> 的平方根。</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模板。等价于 <span class="t-v">(2)</span> （将参数转型为 <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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<tr class="t-par">
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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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<p>若不出现错误，则返回 <code>arg</code> 的平方根（ <span class="mjax" style="display:none">\({\small \sqrt{arg} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;"><span class="t-mrad"><span>√</span><span>arg</span></span></span> ）。</p>
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<p>若出现定义域错误，则返回实现定义值（支持的平台上为 NaN ）。</p>
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<p>若出现下溢所致的值域错误，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 <code>arg</code> 小于零则出现定义域错误。</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>若参数小于 -0 ，则引发 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span> 并返回 NaN 。</li>
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<li>若参数为 +∞ 或 ±0 ，则返回不修改的参数。</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>IEEE 标准要求 <code>std::sqrt</code> 为准确。其他要求为准确的运算只有<a href="cpp-language-operator_arithmetic.html">算术运算符</a>和函数 <span class="t-lc"><a href="cpp-numeric-math-fma.html">std::fma</a></span> 。舍入到返回类型后（用默认舍入模式）， <code>std::sqrt</code> 的结果与无限精度结果不可辨别。换言之，误差小于 0.5 ulp 。其他函数，含 <span class="t-lc"><a href="cpp-numeric-math-pow.html">std::pow</a></span> ，不受这种制约。</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 <cerrno></span>
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<span class="co2">#include <cfenv></span>
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<span class="co2">#include <cstring></span>
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<span class="co2">#pragma STDC FENV_ACCESS ON</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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<span class="co1">// 正常使用</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">"sqrt(100) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">sqrt</span><span class="br0">(</span><span class="nu0">100</span><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">"sqrt(2) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">sqrt</span><span class="br0">(</span><span class="nu0">2</span><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">"golden ratio = "</span> <span class="sy1"><<</span> <span class="br0">(</span><span class="nu0">1</span><span class="sy2">+</span>std<span class="sy4">::</span><span class="me2">sqrt</span><span class="br0">(</span><span class="nu0">5</span><span class="br0">)</span><span class="br0">)</span><span class="sy2">/</span><span class="nu0">2</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
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<span class="co1">// 特殊值</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">"sqrt(-0) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">sqrt</span><span class="br0">(</span><span class="sy2">-</span><span class="nu16">0.0</span><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="co1">// 错误处理</span>
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<span class="kw2">errno</span> <span class="sy1">=</span> <span class="nu0">0</span><span class="sy4">;</span>
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<a href="cpp-numeric-fenv-feclearexcept.html"><span class="kw1449">std::<span class="me2">feclearexcept</span></span></a><span class="br0">(</span><a href="cpp-numeric-fenv-FE_exceptions.html"><span class="kw1460">FE_ALL_EXCEPT</span></a><span class="br0">)</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">"sqrt(-1.0) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">sqrt</span><span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span><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="kw1">if</span><span class="br0">(</span><span class="kw2">errno</span> <span class="sy1">==</span> <a href="cpp-error-errno_macros.html"><span class="kw810">EDOM</span></a><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">" errno = EDOM "</span> <span class="sy1"><<</span> <a href="cpp-string-byte-strerror.html"><span class="kw1161">std::<span class="me2">strerror</span></span></a><span class="br0">(</span><span class="kw2">errno</span><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="kw1">if</span><span class="br0">(</span><a href="cpp-numeric-fenv-fetestexcept.html"><span class="kw1450">std::<span class="me2">fetestexcept</span></span></a><span class="br0">(</span><a href="cpp-numeric-fenv-FE_exceptions.html"><span class="kw1463">FE_INVALID</span></a><span class="br0">)</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">" FE_INVALID raised<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>可能的输出：</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">sqrt(100) = 10
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sqrt(2) = 1.41421
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golden ratio = 1.61803
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sqrt(-0) = -0
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sqrt(-1.0) = -nan
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errno = EDOM Numerical argument out of domain
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FE_INVALID raised</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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<tr class="t-dsc">
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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-pow.html"><span class="t-lines"><span>pow</span><span>powf</span><span>powl</span></span></a></div>
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<div><span class="t-lines"><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>求某数的给定次幂（ <span class="mjax" style="display:none">\(\small{x^y}\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">x<sup>y</sup></span> ）<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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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-cbrt.html"><span class="t-lines"><span>cbrt</span><span>cbrtf</span><span>cbrtl</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>计算立方根（ <span class="mjax" style="display:none">\(\small{\sqrt[3]{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;"><span class="t-mrad"><span>3</span><span>√</span><span>x</span></span></span> ）<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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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-hypot.html"><span class="t-lines"><span>hypot</span><span>hypotf</span><span>hypotl</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>计算两个给定数的平方和的平方根（ <span class="mjax" style="display:none">\(\scriptsize{\sqrt{x^2+y^2} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;"><span class="t-mrad"><span>√</span><span>x<span class="t-su">2<br /></span>+y<span class="t-su">2<br /></span></span></span></span> ）<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-sqrt.html"><span class="t-lines"><span>sqrt<span class="t-dsc-small">(std::complex)</span></span></span></a></div>
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</div>
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</td>
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<td>右半平面范围中的复平方根<br />
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<span class="t-mark">(函数模板)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-valarray-sqrt.html"><span class="t-lines"><span>sqrt<span class="t-dsc-small">(std::valarray)</span></span></span></a></div>
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</div>
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</td>
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<td>应用函数 <span class="t-lc"><strong class="selflink">std::sqrt</strong></span> 到 valarray 的每个元素<br />
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<span class="t-mark">(函数模板)</span></td>
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</tr>
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</table>
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</div>
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<div class="visualClear"></div>
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</div>
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</div>
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</div>
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</body>
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</html>
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