251 lines
16 KiB
HTML
251 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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<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>编译时有理数算术</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_ratio 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">编译时有理数算术</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></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>类模板 <code>std::ratio</code> 及相关的模板提供编译时有理数算术支持。此模板的每个实例化都准确表示任一有限有理数。</p>
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<h3><span class="mw-headline" id=".E7.BC.96.E8.AF.91.E6.97.B6.E5.88.86.E6.95.B0">编译时分数</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-ratio.html"><ratio></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-ratio-ratio.html"><span class="t-lines"><span>ratio</span></span></a></div>
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</div>
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</td>
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<td>表示准确的分数<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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<p>标准库为提供数种对应 SI 比例的便利 typedef :</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-ratio.html"><ratio></a></code></div>
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</td>
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</tr>
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<tr class="t-dsc-hitem">
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<td>类型</td>
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<td>定义</td>
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</tr>
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<tr class="t-dsc">
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<td><code>yocto</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1</span>, <span class="nu0">1000000000000000000000000</span><span class="sy1">></span></span></span> ,若 <span class="t-lc"><a href="cpp-types-integer.html">std::intmax_t</a></span> 能表示分母</td>
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</tr>
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<tr class="t-dsc">
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<td><code>zepto</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1</span>, <span class="nu0">1000000000000000000000</span><span class="sy1">></span></span></span> ,若 <span class="t-lc"><a href="cpp-types-integer.html">std::intmax_t</a></span> 能表示分母</td>
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</tr>
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<tr class="t-dsc">
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<td><code>atto</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1</span>, <span class="nu0">1000000000000000000</span><span class="sy1">></span></span></span></td>
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</tr>
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<tr class="t-dsc">
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<td><code>femto</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1</span>, <span class="nu0">1000000000000000</span><span class="sy1">></span></span></span></td>
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</tr>
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<tr class="t-dsc">
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<td><code>pico</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1</span>, <span class="nu0">1000000000000</span><span class="sy1">></span></span></span></td>
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</tr>
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<tr class="t-dsc">
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<td><code>nano</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1</span>, <span class="nu0">1000000000</span><span class="sy1">></span></span></span></td>
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</tr>
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<tr class="t-dsc">
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<td><code>micro</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1</span>, <span class="nu0">1000000</span><span class="sy1">></span></span></span></td>
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</tr>
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<tr class="t-dsc">
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<td><code>milli</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1</span>, <span class="nu0">1000</span><span class="sy1">></span></span></span></td>
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</tr>
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<tr class="t-dsc">
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<td><code>centi</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1</span>, <span class="nu0">100</span><span class="sy1">></span></span></span></td>
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</tr>
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<tr class="t-dsc">
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<td><code>deci</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1</span>, <span class="nu0">10</span><span class="sy1">></span></span></span></td>
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</tr>
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<tr class="t-dsc">
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<td><code>deca</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">10</span>, <span class="nu0">1</span><span class="sy1">></span></span></span></td>
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</tr>
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<tr class="t-dsc">
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<td><code>hecto</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">100</span>, <span class="nu0">1</span><span class="sy1">></span></span></span></td>
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</tr>
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<tr class="t-dsc">
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<td><code>kilo</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1000</span>, <span class="nu0">1</span><span class="sy1">></span></span></span></td>
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</tr>
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<tr class="t-dsc">
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<td><code>mega</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1000000</span>, <span class="nu0">1</span><span class="sy1">></span></span></span></td>
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</tr>
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<tr class="t-dsc">
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<td><code>giga</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1000000000</span>, <span class="nu0">1</span><span class="sy1">></span></span></span></td>
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</tr>
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<tr class="t-dsc">
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<td><code>tera</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1000000000000</span>, <span class="nu0">1</span><span class="sy1">></span></span></span></td>
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</tr>
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<tr class="t-dsc">
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<td><code>peta</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1000000000000000</span>, <span class="nu0">1</span><span class="sy1">></span></span></span></td>
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</tr>
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<tr class="t-dsc">
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<td><code>exa</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1000000000000000000</span>, <span class="nu0">1</span><span class="sy1">></span></span></span></td>
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</tr>
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<tr class="t-dsc">
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<td><code>zetta</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1000000000000000000000</span>, <span class="nu0">1</span><span class="sy1">></span></span></span> ,若 <span class="t-lc"><a href="cpp-types-integer.html">std::intmax_t</a></span> 能表示分子</td>
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</tr>
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<tr class="t-dsc">
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<td><code>yotta</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-ratio-ratio.html"><span class="kw1522">std::<span class="me2">ratio</span></span></a><span class="sy1"><</span><span class="nu0">1000000000000000000000000</span>, <span class="nu0">1</span><span class="sy1">></span></span></span> ,若 <span class="t-lc"><a href="cpp-types-integer.html">std::intmax_t</a></span> 能表示分子</td>
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</tr>
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</table>
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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">编译时有理数算术</span></h3>
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<p>提供数个别名模板,它们在编译时进行 <code>ratio</code> 实例上的算术。</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-ratio.html"><ratio></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-ratio-ratio_add.html"><span class="t-lines"><span>ratio_add</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>在编译时相加两个 <code>ratio</code> 对象<br />
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<span class="t-mark">(别名模板)</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-ratio-ratio_subtract.html"><span class="t-lines"><span>ratio_subtract</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>在编译时相减两个 <code>ratio</code> 对象<br />
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<span class="t-mark">(别名模板)</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-ratio-ratio_multiply.html"><span class="t-lines"><span>ratio_multiply</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>在编译时相乘两个 <code>ratio</code> 对象<br />
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<span class="t-mark">(别名模板)</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-ratio-ratio_divide.html"><span class="t-lines"><span>ratio_divide</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>在编译时相除两个 <code>ratio</code> 对象<br />
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<span class="t-mark">(别名模板)</span></td>
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</tr>
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</table>
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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.E6.AF.94.E8.BE.83">编译时有理数比较</span></h3>
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<p>提供数个类模板,它们在编译时进行 <code>ratio</code> 实例上的比较运算。</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-ratio.html"><ratio></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-ratio-ratio_equal.html"><span class="t-lines"><span>ratio_equal</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>在编译时比较两个 <code>ratio</code> 对象的相等性<br />
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<span class="t-mark">(类模板)</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-ratio-ratio_not_equal.html"><span class="t-lines"><span>ratio_not_equal</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>在编译时比较两个 <code>ratio</code> 对象的不相等性<br />
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<span class="t-mark">(类模板)</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-ratio-ratio_less.html"><span class="t-lines"><span>ratio_less</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>在编译时比较两个 <code>ratio</code> 对象的<i>小于</i>关系<br />
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<span class="t-mark">(类模板)</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-ratio-ratio_less_equal.html"><span class="t-lines"><span>ratio_less_equal</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>在编译时比较两个 <code>ratio</code> 对象的<i>小于或等于</i>关系<br />
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<span class="t-mark">(类模板)</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-ratio-ratio_greater.html"><span class="t-lines"><span>ratio_greater</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>在编译时比较两个 <code>ratio</code> 对象的<i>大于</i>关系<br />
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<span class="t-mark">(类模板)</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-ratio-ratio_greater_equal.html"><span class="t-lines"><span>ratio_greater_equal</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>在编译时比较两个 <code>ratio</code> 对象的<i>大于或等于</i>关系<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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</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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