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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>asinh<span style="font-size:0.7em; line-height:130%">(std::complex)</span></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-complex.html">complex</a></span></div>
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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></td>
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<td></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw1">template</span><span class="sy1"><</span> <span class="kw1">class</span> T <span class="sy1">></span><br />
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complex<span class="sy1"><</span>T<span class="sy1">></span> asinh<span class="br0">(</span> <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span> z <span class="br0">)</span><span class="sy4">;</span></span></div>
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<td class="t-dcl-nopad"></td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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<td></td>
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<p>计算 <code>z</code> 的复反双曲正弦，分支切割在沿虚轴的 <span class="texhtml" style="white-space: nowrap;">[−i; +i]</span> 区间外。</p>
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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>z</td>
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<td>-</td>
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<td>复数值</td>
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</tr>
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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>z</code> 的复反双曲正弦，在沿实轴数学上无界，沿虚轴在区间 <span class="texhtml" style="white-space: nowrap;">[−iπ/2; +iπ/2]</span> 中的条状范围中。</p>
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<h3><span class="mw-headline" id=".E9.94.99.E8.AF.AF.E5.A4.84.E7.90.86.E5.8F.8A.E7.89.B9.E6.AE.8A.E5.80.BC">错误处理及特殊值</span></h3>
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<p>报告的错误与 <a href="cpp-numeric-math-math_errhandling.html"><tt>math_errhandling</tt></a> 一致。</p>
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<p>若实现支持 IEEE 浮点算术，则</p>
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<ul>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-math-asinh.html"><span class="kw1343">std::<span class="me2">asinh</span></span></a><span class="br0">(</span>std<span class="sy4">::</span><span class="me2">conj</span><span class="br0">(</span>z<span class="br0">)</span><span class="br0">)</span> <span class="sy1">==</span> std<span class="sy4">::</span><span class="me2">conj</span><span class="br0">(</span><a href="cpp-numeric-math-asinh.html"><span class="kw1343">std::<span class="me2">asinh</span></span></a><span class="br0">(</span>z<span class="br0">)</span><span class="br0">)</span></span></span></li>
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<li><span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-math-asinh.html"><span class="kw1343">std::<span class="me2">asinh</span></span></a><span class="br0">(</span><span class="sy2">-</span>z<span class="br0">)</span> <span class="sy1">==</span> <span class="sy2">-</span><a href="cpp-numeric-math-asinh.html"><span class="kw1343">std::<span class="me2">asinh</span></span></a><span class="br0">(</span>z<span class="br0">)</span></span></span></li>
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<li>若 <code>z</code> 为 <code>(+0,+0)</code> ，则结果为 <code>(+0,+0)</code></li>
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<li>若 <code>z</code> 为 <code>(x,+∞)</code> （对于任何有限正 x ），则结果为 <code>(+∞,π/2)</code></li>
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<li>若 <code>z</code> 为 <code>(x,NaN)</code> （对于任何有限 x ），则结果为 <code>(NaN,NaN)</code> 并可能引发 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span></li>
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<li>若 <code>z</code> 为 <code>(+∞,y)</code> （对于任何有限正 y ），则结果为 <code>(+∞,+0)</code></li>
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<li>若 <code>z</code> 为 <code>(+∞,+∞)</code> ，则结果为 <code>(+∞,π/4)</code></li>
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<li>若 <code>z</code> 为 <code>(+∞,NaN)</code> ，则结果为 <code>(+∞,NaN)</code></li>
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<li>若 <code>z</code> 为 <code>(NaN,+0)</code> ，则结果为 <code>(NaN,+0)</code></li>
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<li>若 <code>z</code> 为 <code>(NaN,y)</code> （对于任何有限非零 y ），则结果为 <code>(NaN,NaN)</code> 并可能引发 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span></li>
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<li>若 <code>z</code> 为 <code>(NaN,+∞)</code> ，则结果为 <code>(±∞,NaN)</code> （实部符号未指定）</li>
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<li>若 <code>z</code> 为 <code>(NaN,NaN)</code> ，则结果为 <code>(NaN,NaN)</code></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++ 标准命名此函数为“复弧双曲正弦”函数，双曲函数的反函数仍是面积函数。其参数是双曲扇形的面积，而非弧长。正确的名称是“复反双曲正弦”或较不常用的“复面积双曲正弦”。</p>
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<p>反双曲正弦是多值函数，而在复平面上要求分支切割。约定将分支置于虚轴的线段 <span class="texhtml" style="white-space: nowrap;">(-<i>i</i>∞,-<i>i</i>)</span> 和 <span class="texhtml" style="white-space: nowrap;">(<i>i</i>,<i>i</i>∞)</span> 上。</p>
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<p>反双曲正弦主值的数学定义是 <span class="texhtml" style="white-space: nowrap;">asinh z = ln(z + <span class="t-mrad"><span>√</span><span>1+z<span class="t-su">2<br /></span></span></span>)</span> 。</p>
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对于任何 z ， <span class="texhtml" style="white-space: nowrap;">asinh(z) = <span class="t-mfrac"></span></span>
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<table>
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<tr>
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<td>asin(iz)</td>
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</tr>
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<tr>
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<td>i</td>
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</table>
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。
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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 <complex></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="kw1758">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1784">std::<span class="me2">fixed</span></span></a><span class="sy4">;</span>
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<a href="cpp-numeric-complex.html"><span class="kw1472">std::<span class="me2">complex</span></span></a><span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span> z1<span class="br0">(</span><span class="nu0">0</span>, <span class="sy2">-</span><span class="nu0">2</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="cpp-io-cout.html"><span class="kw1758">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"asinh"</span> <span class="sy1"><<</span> z1 <span class="sy1"><<</span> <span class="st0">" = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-math-asinh.html"><span class="kw1343">std::<span class="me2">asinh</span></span></a><span class="br0">(</span>z1<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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<a href="cpp-numeric-complex.html"><span class="kw1472">std::<span class="me2">complex</span></span></a><span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span> z2<span class="br0">(</span><span class="sy2">-</span><span class="nu16">0.0</span>, <span class="sy2">-</span><span class="nu0">2</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="cpp-io-cout.html"><span class="kw1758">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"asinh"</span> <span class="sy1"><<</span> z2 <span class="sy1"><<</span> <span class="st0">" (the other side of the cut) = "</span>
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<span class="sy1"><<</span> <a href="cpp-numeric-math-asinh.html"><span class="kw1343">std::<span class="me2">asinh</span></span></a><span class="br0">(</span>z2<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">// 对于任何 z ， asinh(z) = asin(iz)/i</span>
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<a href="cpp-numeric-complex.html"><span class="kw1472">std::<span class="me2">complex</span></span></a><span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span> z3<span class="br0">(</span><span class="nu0">1</span>,<span class="nu0">2</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="cpp-numeric-complex.html"><span class="kw1472">std::<span class="me2">complex</span></span></a><span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span> i<span class="br0">(</span><span class="nu0">0</span>,<span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="cpp-io-cout.html"><span class="kw1758">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"asinh"</span> <span class="sy1"><<</span> z3 <span class="sy1"><<</span> <span class="st0">" = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-math-asinh.html"><span class="kw1343">std::<span class="me2">asinh</span></span></a><span class="br0">(</span>z3<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">"asin"</span> <span class="sy1"><<</span> z3<span class="sy2">*</span>i <span class="sy1"><<</span> <span class="st0">"/i = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-math-asin.html"><span class="kw1336">std::<span class="me2">asin</span></span></a><span class="br0">(</span>z3<span class="sy2">*</span>i<span class="br0">)</span><span class="sy2">/</span>i <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">asinh(0.000000,-2.000000) = (1.316958,-1.570796)
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asinh(-0.000000,-2.000000) (the other side of the cut) = (-1.316958,-1.570796)
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asinh(1.000000,2.000000) = (1.469352,1.063440)
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asin(-2.000000,1.000000)/i = (1.469352,1.063440)</pre></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-complex-acosh.html"><span class="t-lines"><span>acosh<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>计算复数的反双曲余弦（ <span class="mjax" style="display:none">\({\small\operatorname{arcosh}{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arcosh(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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<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-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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<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-sinh.html"><span class="t-lines"><span>sinh<span class="t-dsc-small">(std::complex)</span></span></span></a></div>
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</div>
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</td>
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<td>计算复数的双曲正弦（ <span class="mjax" style="display:none">\({\small\sinh{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">sinh(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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<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-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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</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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