239 lines
19 KiB
HTML
239 lines
19 KiB
HTML
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<title>std::atan2, std::atan2f, std::atan2l</title>
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<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-cpp_numeric_math_atan2 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>atan2, <span style="font-size:0.7em; line-height:130%">std::</span>atan2f, <span style="font-size:0.7em; line-height:130%">std::</span>atan2l</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></td>
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<td></td>
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<td rowspan="142">(1)</td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">float</span> atan2 <span class="br0">(</span> <span class="kw4">float</span> y, <span class="kw4">float</span> x <span class="br0">)</span><span class="sy4">;</span></span></div>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">float</span> atan2f<span class="br0">(</span> <span class="kw4">float</span> y, <span class="kw4">float</span> x <span class="br0">)</span><span class="sy4">;</span></span></div>
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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> atan2 <span class="br0">(</span> <span class="kw4">double</span> y, <span class="kw4">double</span> x <span class="br0">)</span><span class="sy4">;</span></span></div>
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<td>(2)</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> atan2 <span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> y, <span class="kw4">long</span> <span class="kw4">double</span> x <span class="br0">)</span><span class="sy4">;</span></span></div>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span> atan2l<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> y, <span class="kw4">long</span> <span class="kw4">double</span> x <span class="br0">)</span><span class="sy4">;</span></span></div>
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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">Promoted atan2 <span class="br0">(</span> Arithmetic1 y, Arithmetic2 x <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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<div class="t-li1"><span class="t-li">1-3)</span> 计算 <code>y/x</code> 的弧（反）正切，以参数符号确定正确的象限。</div>
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<div class="t-li1"><span class="t-li">4)</span> 所有 1-3) 所不覆盖的算术类型的重载集或函数模板。若任何参数拥有<a href="cpp-types-is_integral.html">整数类型</a>，则将它转型为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> 。若任何参数为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span></span></span> ，则返回类型 <code>Promoted</code> 亦为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span></span></span> ，否则返回类型始终为 <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>x, y</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>y/x</code> 在 <span class="texhtml" style="white-space: nowrap;">[-π ; +π]</span> 弧度范围中的弧（反）正切（ <span class="texhtml" style="white-space: nowrap;">arctan(<span class="t-mfrac"></span></span>
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<table>
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<td>y</td>
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<td>x</td>
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) ）。
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<div class="t-plot">
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<div class="t-plot-left">Y 参数</div>
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<div class="t-plot-right">返回值</div>
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<div class="t-plot-bottom">X 参数</div>
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</div>
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<p>若出现定义域错误，则返回实现定义值。</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>x</code> 与 <code>y</code> 均为零则可能出现定义域错误。</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 <code>x</code> 与 <code>y</code> 均为零，则定义域错误<i>不出现</i></li>
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<li>若 <code>x</code> 与 <code>y</code> 均为零，则也不出现值域错误</li>
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<li>若 <code>y</code> 为零，则不出现极点错误</li>
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<li>若 <code>y</code> 为 <code>±0</code> 且 <code>x</code> 为负或 <code>-0</code> ，则返回 <code>±π</code></li>
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<li>若 <code>y</code> 为 <code>±0</code> 且 <code>x</code> 为正或 <code>+0</code> ，则返回 <code>±0</code></li>
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<li>若 <code>y</code> 为 <code>±∞</code> 且 <code>x</code> 有限，则返回 <code>±π/2</code></li>
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<li>若 <code>y</code> 为 <code>±∞</code> 且 <code>x</code> 为 <code>-∞</code> ，则返回 <code>±3π/4</code></li>
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<li>若 <code>y</code> 为 <code>±∞</code> 且 <code>x</code> 为 <code>+∞</code> ，则返回 <code>±π/4</code></li>
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<li>若 <code>x</code> 为 <code>±0</code> 且 <code>y</code> 为负，则返回 <code>-π/2</code></li>
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<li>若 <code>x</code> 为 <code>±0</code> 且 <code>y</code> 为正，则返回 <code>+π/2</code></li>
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<li>若 <code>x</code> 为 <code>-∞</code> 且 <code>y</code> 为正有限，则返回 <code>+π</code></li>
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<li>若 <code>x</code> 为 <code>-∞</code> 且 <code>y</code> 为负有限，则返回 <code>-π</code></li>
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<li>若 <code>x</code> 为 <code>+∞</code> 且 <code>y</code> 为正有限，则返回 <code>+0</code></li>
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<li>若 <code>x</code> 为 <code>+∞</code> 且 <code>y</code> 为负有限，则返回 <code>-0</code></li>
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<li>若 <code>x</code> 为 NaN 或 <code>y</code> 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><span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">atan2</span><span class="br0">(</span>y, x<span class="br0">)</span></span></span> 等价于 <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">arg</span><span class="br0">(</span><a href="cpp-numeric-complex.html"><span class="kw1471">std::<span class="me2">complex</span></span></a><span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="br0">(</span>x,y<span class="br0">)</span><span class="br0">)</span></span></span> 。</p>
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<p><a rel="nofollow" class="external text" href="http://pubs.opengroup.org/onlinepubs/9699919799/functions/atan2.html">POSIX 指定</a>在下溢情况下，返回不修改的 <code>arg</code> ，而若不支持如此，则返回不大于 DBL_MIN 、 FLT_MIN 和 LDBL_MIN 的实现定义值。</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="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">// 正常用法：二个参数的符号确定象限</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">"(+1,+1) cartesian is ("</span> <span class="sy1"><<</span> hypot<span class="br0">(</span><span class="nu0">1</span>,<span class="nu0">1</span><span class="br0">)</span>
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<span class="sy1"><<</span> <span class="st0">','</span> <span class="sy1"><<</span> atan2<span class="br0">(</span><span class="nu0">1</span>,<span class="nu0">1</span><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">") polar<span class="es1">\n</span>"</span> <span class="co1">// atan2(1,1) = +pi/4 ，第 I 象限</span>
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<span class="sy1"><<</span> <span class="st0">"(+1,-1) cartesian is ("</span> <span class="sy1"><<</span> hypot<span class="br0">(</span><span class="nu0">1</span>,<span class="sy2">-</span><span class="nu0">1</span><span class="br0">)</span>
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<span class="sy1"><<</span> <span class="st0">','</span> <span class="sy1"><<</span> atan2<span class="br0">(</span><span class="nu0">1</span>,<span class="sy2">-</span><span class="nu0">1</span><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">") polar<span class="es1">\n</span>"</span> <span class="co1">// atan2(1, -1) = +3pi/4 ，第 II 象限</span>
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<span class="sy1"><<</span> <span class="st0">"(-1,-1) cartesian is ("</span> <span class="sy1"><<</span> hypot<span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span>,<span class="sy2">-</span><span class="nu0">1</span><span class="br0">)</span>
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<span class="sy1"><<</span> <span class="st0">','</span> <span class="sy1"><<</span> atan2<span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span>,<span class="sy2">-</span><span class="nu0">1</span><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">") polar<span class="es1">\n</span>"</span> <span class="co1">// atan2(-1,-1) = -3pi/4 ，第 III 象限</span>
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<span class="sy1"><<</span> <span class="st0">"(-1,+1) cartesian is ("</span> <span class="sy1"><<</span> hypot<span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span>,<span class="nu0">1</span><span class="br0">)</span>
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<span class="sy1"><<</span> <span class="st0">','</span> <span class="sy1"><<</span> atan2<span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span>,<span class="nu0">1</span><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">") polar<span class="es1">\n</span>"</span><span class="sy4">;</span> <span class="co1">// atan2(-1,1) = -pi/4 ，第 IV 象限</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">"atan2(0, 0) = "</span> <span class="sy1"><<</span> atan2<span class="br0">(</span><span class="nu0">0</span>,<span class="nu0">0</span><span class="br0">)</span>
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<span class="sy1"><<</span> <span class="st0">" atan2(0,-0) = "</span> <span class="sy1"><<</span> atan2<span class="br0">(</span><span class="nu0">0</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>
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<span class="sy1"><<</span> <span class="st0">"atan2(7, 0) = "</span> <span class="sy1"><<</span> atan2<span class="br0">(</span><span class="nu0">7</span>,<span class="nu0">0</span><span class="br0">)</span>
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<span class="sy1"><<</span> <span class="st0">" atan2(7,-0) = "</span> <span class="sy1"><<</span> atan2<span class="br0">(</span><span class="nu0">7</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="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">(+1,+1) cartesian is (1.41421,0.785398) polar
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(+1,-1) cartesian is (1.41421,2.35619) polar
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(-1,-1) cartesian is (1.41421,-2.35619) polar
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(-1,+1) cartesian is (1.41421,-0.785398) polar
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atan2(0, 0) = 0 atan2(0,-0) = 3.14159
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atan2(7, 0) = 1.5708 atan2(7,-0) = 1.5708</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-asin.html"><span class="t-lines"><span>asin</span><span>asinf</span><span>asinl</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>计算反正弦（ <span class="mjax" style="display:none">\({\small\arcsin{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arcsin(x)</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-acos.html"><span class="t-lines"><span>acos</span><span>acosf</span><span>acosl</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>计算反余弦（ <span class="mjax" style="display:none">\({\small\arccos{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arccos(x)</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-atan.html"><span class="t-lines"><span>atan</span><span>atanf</span><span>atanl</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>计算反正切（ <span class="mjax" style="display:none">\({\small\arctan{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arctan(x)</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-arg.html"><span class="t-lines"><span>arg</span></span></a></div>
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</div>
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</td>
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<td>返回辐角<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-atan2.html"><span class="t-lines"><span>atan2<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::atan2</strong></span> 到一个 valarray 和一个值<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 class="visualClear"></div>
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