405 lines
22 KiB
HTML
405 lines
22 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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<head><meta http-equiv="x-ua-compatible" content="ie=edge">
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
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<title>数值库</title>
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<link rel="stylesheet" href="ext.css" />
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<link rel="stylesheet" href="site_modules.css" />
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</head>
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<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-cpp_numeric skin-cppreference2 action-view cpp-navbar">
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<div id="cpp-content-base">
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<div id="content"><a id="top"></a>
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<h1 id="firstHeading" class="firstHeading">数值库</h1>
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<div id="bodyContent">
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<div id="contentSub"><span class="subpages">< <a href="cpp.html">cpp</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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<p>C++ 数值库包含常用数学函数及类型,以及优化的数值数组及对随机数生成的支持。</p>
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<h2><span class="mw-headline" id=".E6.95.B0.E5.AD.A6.E5.87.BD.E6.95.B0.E4.B8.8E.E7.B1.BB.E5.9E.8B">数学函数与类型</span></h2>
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<h3><span class="mw-headline" id=".E5.B8.B8.E7.94.A8.E6.95.B0.E5.AD.A6.E5.87.BD.E6.95.B0"><a href="cpp-numeric-math.html">常用数学函数</a></span></h3>
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<p>头文件 <a href="cpp-header-cmath.html"><tt><cmath></tt></a> 提供<a href="cpp-numeric-math.html">标准 C 库数学函数</a>,例如 <span class="t-lc"><a href="cpp-numeric-math-fabs.html">std::fabs</a></span> 、 <span class="t-lc"><a href="cpp-numeric-math-sqrt.html">std::sqrt</a></span> 及 <span class="t-lc"><a href="cpp-numeric-math-sin.html">std::sin</a></span> 。</p>
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<h3><span class="mw-headline" id=".E6.95.B0.E5.AD.A6.E7.89.B9.E6.AE.8A.E5.87.BD.E6.95.B0_.28C.2B.2B17_.E8.B5.B7.29"><a href="cpp-numeric-special_functions.html">数学特殊函数</a> <span class="t-mark-rev t-since-cxx17">(C++17 起)</span></span></h3>
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<p>头文件 <a href="cpp-header-cmath.html"><tt><cmath></tt></a> 亦提供数个特殊数学函数,例如 <span class="t-lc"><a href="cpp-numeric-special_math-beta.html" class="mw-redirect">std::beta</a></span> 、 <span class="t-lc"><a href="cpp-numeric-special_math-hermite.html" class="mw-redirect">std::hermite</a></span> 及 <span class="t-lc"><a href="cpp-numeric-special_math-cyl_bessel_i.html" class="mw-redirect">std::cyl_bessel_i</a></span> 。</p>
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<h3><span class="mw-headline" id=".E6.95.B0.E5.AD.A6.E5.B8.B8.E6.95.B0_.28C.2B.2B20_.E8.B5.B7.29"><a href="cpp-numeric-constants.html">数学常数</a> <span class="t-mark-rev t-since-cxx20">(C++20 起)</span></span></h3>
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<p>头文件 <a href="cpp-header-numbers.html"><tt><numbers></tt></a> 提供数个数学常数,例如 <span class="t-lc">std::numbers::pi</span> 或 <span class="t-lc">std::numbers::sqrt2</span> 。</p>
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<h3><span class="mw-headline" id=".E5.A4.8D.E6.95.B0.E7.AE.97.E6.9C.AF">复数算术</span></h3>
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<table class="t-dsc-begin">
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<tr class="t-dsc-header">
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<td colspan="2">
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<div>定义于头文件 <code><a href="cpp-header-complex.html"><complex></a></code></div>
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</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.html"><span class="t-lines"><span>complex</span></span></a></div>
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</div>
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</td>
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<td>复数类型<br />
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<span class="t-mark">(类模板)</span></td>
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</tr>
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</table>
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<h3><span class="mw-headline" id=".E6.95.B0.E5.80.BC.E6.95.B0.E7.BB.84">数值数组</span></h3>
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<table class="t-dsc-begin">
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<tr class="t-dsc-header">
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<td colspan="2">
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<div>定义于头文件 <code><a href="cpp-header-valarray.html"><valarray></a></code></div>
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</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.html"><span class="t-lines"><span>valarray</span></span></a></div>
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</div>
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</td>
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<td>数值数组、数组掩码及数组切片<br />
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<span class="t-mark">(类模板)</span></td>
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</tr>
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</table>
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<h2><span class="mw-headline" id=".E6.95.B0.E5.80.BC.E7.AE.97.E6.B3.95">数值算法</span></h2>
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<p>头文件 <a href="cpp-header-numeric.html"><tt><numeric></tt></a> 提供下列数值算法:</p>
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<h3><span class="mw-headline" id=".E5.9B.A0.E6.95.B0.E8.BF.90.E7.AE.97">因数运算</span></h3>
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<table class="t-dsc-begin">
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<tr class="t-dsc-header">
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<td colspan="2">
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<div>定义于头文件 <code><a href="cpp-header-numeric.html"><numeric></a></code></div>
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</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-gcd.html"><span class="t-lines"><span>gcd</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span></span></div>
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</div>
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</td>
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<td>返回二个整数最大公约数的 <code>constexpr</code> 函数模板<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-lcm.html"><span class="t-lines"><span>lcm</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span></span></div>
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</div>
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</td>
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<td>返回二个整数最小公倍数的 <code>constexpr</code> 函数模板<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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<h3><span class="mw-headline" id=".E6.8F.92.E5.80.BC.E8.BF.90.E7.AE.97">插值运算</span></h3>
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<table class="t-dsc-begin">
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<tr class="t-dsc-header">
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<td colspan="2">
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<div>定义于头文件 <code><a href="cpp-header-numeric.html"><numeric></a></code></div>
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</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-midpoint.html"><span class="t-lines"><span>midpoint</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
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</div>
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</td>
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<td>两个数值或指针间的中点<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-header">
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<td colspan="2">
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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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</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-lerp.html"><span class="t-lines"><span>lerp</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
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</div>
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</td>
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<td>线性插值函数<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=".E6.95.B0.E5.80.BC.E8.BF.90.E7.AE.97">数值运算</span></h3>
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<table class="t-dsc-begin">
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<tr class="t-dsc-header">
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<td colspan="2">
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<div>定义于头文件 <code><a href="cpp-header-numeric.html"><numeric></a></code></div>
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</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-algorithm-iota.html"><span class="t-lines"><span>iota</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></div>
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</div>
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</td>
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<td>用从起始值开始连续递增的值填充一个范围<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-algorithm-accumulate.html"><span class="t-lines"><span>accumulate</span></span></a></div>
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</div>
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</td>
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<td>对一个范围内的元素求和<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-algorithm-reduce.html"><span class="t-lines"><span>reduce</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span></span></div>
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</div>
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</td>
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<td>类似 <span class="t-lc"><a href="cpp-algorithm-accumulate.html">std::accumulate</a></span>,但不依序执行<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-algorithm-transform_reduce.html"><span class="t-lines"><span>transform_reduce</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span></span></div>
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</div>
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</td>
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<td>应用一个函数对象,然后以乱序规约<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-algorithm-inner_product.html"><span class="t-lines"><span>inner_product</span></span></a></div>
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</div>
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</td>
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<td>计算两个范围的元素的内积<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-algorithm-adjacent_difference.html"><span class="t-lines"><span>adjacent_difference</span></span></a></div>
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</div>
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</td>
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<td>计算范围内各相邻元素之间的差<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-algorithm-partial_sum.html"><span class="t-lines"><span>partial_sum</span></span></a></div>
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</div>
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</td>
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<td>计算范围内元素的部分和<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-algorithm-inclusive_scan.html"><span class="t-lines"><span>inclusive_scan</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span></span></div>
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</div>
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</td>
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<td>类似 <span class="t-lc"><a href="cpp-algorithm-partial_sum.html">std::partial_sum</a></span>,第 i 个和中包含第 i 个输入<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-algorithm-exclusive_scan.html"><span class="t-lines"><span>exclusive_scan</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span></span></div>
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</div>
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</td>
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<td>类似 <span class="t-lc"><a href="cpp-algorithm-partial_sum.html">std::partial_sum</a></span>,第 i 个和中排除第 i 个输入<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-algorithm-transform_inclusive_scan.html"><span class="t-lines"><span>transform_inclusive_scan</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span></span></div>
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</div>
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</td>
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<td>应用一个函数对象,然后进行包含扫描<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-algorithm-transform_exclusive_scan.html"><span class="t-lines"><span>transform_exclusive_scan</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span></span></div>
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</div>
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</td>
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<td>应用一个函数对象,然后进行排除扫描<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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<h2><span class="mw-headline" id=".E6.9D.82.E9.A1.B9">杂项</span></h2>
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<h3><span class="mw-headline" id=".E4.BC.AA.E9.9A.8F.E6.9C.BA.E6.95.B0.E7.94.9F.E6.88.90"><a href="cpp-numeric-random.html">伪随机数生成</a></span></h3>
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<p>头文件 <a href="cpp-header-random.html"><tt><random></tt></a> 定义<a href="cpp-numeric-random.html">为随机数生成器与数值分布</a>。头文件 <code>cstdlib</code> 亦包含 C 风格随机数生成,通过 <span class="t-lc"><a href="cpp-numeric-random-srand.html">std::srand</a></span> 和 <span class="t-lc"><a href="cpp-numeric-random-rand.html">std::rand</a></span> 。</p>
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<h3><span class="mw-headline" id=".E7.BC.96.E8.AF.91.E6.97.B6.E6.9C.89.E7.90.86.E6.95.B0.E7.AE.97.E6.9C.AF_.28C.2B.2B11_.E8.B5.B7.29"><a href="cpp-numeric-ratio.html">编译时有理数算术</a> <span class="t-mark-rev t-since-cxx11">(C++11 起)</span></span></h3>
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<p>头文件 <a href="cpp-header-ratio.html"><tt><ratio></tt></a> 提供<a href="cpp-numeric-ratio.html">操作和存储编译时比例的类型和函数</a>。</p>
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<h3><span class="mw-headline" id=".E6.B5.AE.E7.82.B9.E7.8E.AF.E5.A2.83_.28C.2B.2B11_.E8.B5.B7.29"><a href="cpp-numeric-fenv.html">浮点环境</a> <span class="t-mark-rev t-since-cxx11">(C++11 起)</span></span></h3>
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<p>头文件 <a href="cpp-header-cfenv.html"><tt><cfenv></tt></a> 定义<a href="cpp-numeric-fenv.html">关系到异常浮点状态的标志和函数</a>,例如上溢和除以零。</p>
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<h3><span class="mw-headline" id=".E4.BD.8D.E6.93.8D.E7.BA.B5_.28C.2B.2B20_.E8.B5.B7.29">位操纵 <span class="t-mark-rev t-since-cxx20">(C++20 起)</span></span></h3>
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<p>头文件 <a href="cpp-header-bit.html"><tt><bit></tt></a> 提供数个访问、操纵及处理单独位和位序列的函数模板。</p>
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<table class="t-dsc-begin">
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<tr class="t-dsc-header">
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<td colspan="2">
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<div>定义于头文件 <code><a href="cpp-header-bit.html"><bit></a></code></div>
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</td>
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</tr>
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<tr class="t-dsc-header">
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<td colspan="2">
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<div>定义于命名空间 <code>std</code></div>
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</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-bit_cast.html"><span class="t-lines"><span>bit_cast</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
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</div>
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</td>
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<td>将一个类型的对象表示重解释为另一类型的对象表示<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-byteswap.html"><span class="t-lines"><span>byteswap</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx23">(C++23)</span></span></span></div>
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</div>
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</td>
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<td>反转给定整数值中的字节<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-has_single_bit.html"><span class="t-lines"><span>has_single_bit</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
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</div>
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</td>
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<td>检查一个数是否为二的整数次幂<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-bit_ceil.html"><span class="t-lines"><span>bit_ceil</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
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</div>
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</td>
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<td>寻找不小于给定值的最小的二的整数次幂<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-bit_floor.html"><span class="t-lines"><span>bit_floor</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
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</div>
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</td>
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<td>寻找不大于给定值的最大的二的整数次幂<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-bit_width.html"><span class="t-lines"><span>bit_width</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
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</div>
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</td>
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<td>寻找表示给定值所需的最小位数<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-rotl.html"><span class="t-lines"><span>rotl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
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</div>
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</td>
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<td>计算逐位左旋转的结果<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-rotr.html"><span class="t-lines"><span>rotr</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
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</div>
|
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</td>
|
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<td>计算逐位右旋转的结果<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-countl_zero.html"><span class="t-lines"><span>countl_zero</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
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</div>
|
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</td>
|
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<td>从最高位起计量连续的 0 位的数量<br />
|
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<span class="t-mark">(函数模板)</span></td>
|
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</tr>
|
|
<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-countl_one.html"><span class="t-lines"><span>countl_one</span></span></a></div>
|
|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
|
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</div>
|
|
</td>
|
|
<td>从最高位起计量连续的 1 位的数量<br />
|
|
<span class="t-mark">(函数模板)</span></td>
|
|
</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="cpp-numeric-countr_zero.html"><span class="t-lines"><span>countr_zero</span></span></a></div>
|
|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
|
|
</div>
|
|
</td>
|
|
<td>从最低位起计量连续的 0 位的数量<br />
|
|
<span class="t-mark">(函数模板)</span></td>
|
|
</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="cpp-numeric-countr_one.html"><span class="t-lines"><span>countr_one</span></span></a></div>
|
|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
|
|
</div>
|
|
</td>
|
|
<td>从最低位起计量连续的 1 位的数量<br />
|
|
<span class="t-mark">(函数模板)</span></td>
|
|
</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="cpp-numeric-popcount.html"><span class="t-lines"><span>popcount</span></span></a></div>
|
|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
|
|
</div>
|
|
</td>
|
|
<td>计量无符号整数中为 1 的位的数量<br />
|
|
<span class="t-mark">(函数模板)</span></td>
|
|
</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="cpp-types-endian.html"><span class="t-lines"><span>endian</span></span></a></div>
|
|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
|
|
</div>
|
|
</td>
|
|
<td>指示标量类型的端序<br />
|
|
<span class="t-mark">(枚举)</span></td>
|
|
</tr>
|
|
</table>
|
|
<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"></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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