181 lines
16 KiB
HTML
181 lines
16 KiB
HTML
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<title>std::atanh, std::atanh, std::atanhl</title>
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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>atanh, <span style="font-size:0.7em; line-height:130%">std::</span>atanh, <span style="font-size:0.7em; line-height:130%">std::</span>atanhl</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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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">float</span> atanh <span class="br0">(</span> <span class="kw4">float</span> arg <span class="br0">)</span><span class="sy4">;</span><br />
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<span class="kw4">float</span> atanhf<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>(1)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span> atanh <span class="br0">(</span> <span class="kw4">double</span> arg <span class="br0">)</span><span class="sy4">;</span></span></div>
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<td>(2)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span> atanh <span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> arg <span class="br0">)</span><span class="sy4">;</span><br />
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<span class="kw4">long</span> <span class="kw4">double</span> atanhl<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> arg <span class="br0">)</span><span class="sy4">;</span></span></div>
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<td>(3)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span> atanh <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 class="t-dcl-sep">
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<div class="t-li1"><span class="t-li">1-3)</span> 计算 <code>arg</code> 的反正切。</div>
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<div class="t-li1"><span class="t-li">4)</span> 接受任何<a href="cpp-types-is_integral.html">整数类型</a>参数的重载集或函数模板。等价于 2) （将参数转型到 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> ）。</div>
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<h3><span class="mw-headline" id=".E5.8F.82.E6.95.B0">参数</span></h3>
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<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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<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> 的反双曲正切（ <span class="texhtml" style="white-space: nowrap;">tanh<span class="t-su">-1<br /></span>(arg)</span> 或 <span class="texhtml" style="white-space: nowrap;">artanh(arg)</span> ）。</p>
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<p>若出现定义域错误，则返回实现定义值（若支持则为 NaN ）。</p>
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<p>若出现极点错误，则返回 <code>±HUGE_VAL</code> 、 <code>±HUGE_VALF</code> 或 <code>±HUGE_VALL</code> （带正确符号）。</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>若参数不在区间 <span class="texhtml" style="white-space: nowrap;">[-1, +1]</span> 中，则出现值域错误。</p>
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<p>若参数为 ±1 ，则出现极点错误。</p>
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<p>若实现支持 IEEE 浮点算术（ IEC 60559 ），则</p>
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<ul>
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<li>若参数为 ±0 ，则返回不修改的参数。</li>
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<li>若参数为 ±1 ，则返回 ±∞ 并引发 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_DIVBYZERO</a></span> 。</li>
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<li>若 <span class="texhtml" style="white-space: nowrap;">|arg|>1</span> ，则返回 NaN 并引发 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span> 。</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.E6.84.8F">注意</span></h3>
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<p>尽管（ C++ 对此函数引用的） C 标准命名此函数为“弧双曲正切”，双曲函数的反函数是面积函数。其参数为双曲扇形的面积，而非弧。正确的名称为“反双曲正切”（ POSIX 所用）或“面积双曲正切”。</p>
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<p><a rel="nofollow" class="external text" href="http://pubs.opengroup.org/onlinepubs/9699919799/functions/atanh.html">POSIX 指定</a>在下溢的情况下，返回不修改的 <code>arg</code> ，而且若不支持，则返回不大于 DBL_MIN 、 FLT_MIN 和 LDBL_MIN 的值。</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="co2">#include <cfloat></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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<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"atanh(0) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">atanh</span><span class="br0">(</span><span class="nu0">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">"atanh(-0) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">atanh</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>
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<span class="sy1"><<</span> <span class="st0">"atanh(0.9) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">atanh</span><span class="br0">(</span><span class="nu16">0.9</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">"atanh(-1) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">atanh</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="kw862">ERANGE</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 == ERANGE: "</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="kw1461">FE_DIVBYZERO</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_DIVBYZERO 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">atanh(0) = 0
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atanh(-0) = -0
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atanh(0.9) = 1.47222
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atanh(-1) = -inf
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errno == ERANGE: Numerical result out of range
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FE_DIVBYZERO 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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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-math-asinh.html"><span class="t-lines"><span>asinh</span><span>asinhf</span><span>asinhl</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>计算反双曲正弦（ <span class="mjax" style="display:none">\({\small\operatorname{arsinh}{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arsinh(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-acosh.html"><span class="t-lines"><span>acosh</span><span>acoshf</span><span>acoshl</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>计算反双曲余弦（ <span class="mjax" style="display:none">\({\small\operatorname{arcosh}{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arcosh(x)</span> ）<br />
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<span class="t-mark">(函数)</span></td>
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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-tanh.html"><span class="t-lines"><span>tanh</span><span>tanhf</span><span>tanhl</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>计算双曲正切（ <span class="mjax" style="display:none">\({\small\tanh{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">tanh(x)</span> ）<br />
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<span class="t-mark">(函数)</span></td>
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<tr class="t-dsc">
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-atanh.html"><span class="t-lines"><span>atanh<span class="t-dsc-small">(std::complex)</span></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>计算复数的反双曲正切（ <span class="mjax" style="display:none">\({\small\operatorname{artanh}{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">artanh(z)</span> ）<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=".E5.A4.96.E9.83.A8.E9.93.BE.E6.8E.A5">外部链接</span></h3>
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<p><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/InverseHyperbolicTangent.html">Weisstein, Eric W. “反双曲正切。”</a>来自 MathWorld--A Wolfram Web Resource 。</p>
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</div>
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<div class="visualClear"></div>
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