253 lines
17 KiB
HTML
253 lines
17 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>ctanhf, ctanh, ctanhl</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-c_numeric_complex_ctanh 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">ctanhf, ctanh, ctanhl</h1>
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<div id="bodyContent">
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<div id="contentSub"><span class="subpages">< <a href="c.html">c</a>‎ | <a href="c-numeric.html">numeric</a>‎ | <a href="c-numeric-complex.html">complex</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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<table class="t-dcl-begin">
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<tr class="t-dsc-header">
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<td>
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<div>定义于头文件 <code><complex.h></code></div>
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</td>
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<td></td>
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<td></td>
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</tr>
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<tr class="t-dcl t-since-c99">
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<div><span class="mw-geshi c source-c"><span class="kw4">float</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a> ctanhf<span class="br0">(</span> <span class="kw4">float</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a> z <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(1)</td>
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<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
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</tr>
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<tr class="t-dcl t-since-c99">
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<td>
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<div><span class="mw-geshi c source-c"><span class="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a> ctanh<span class="br0">(</span> <span class="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a> z <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(2)</td>
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<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
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</tr>
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<tr class="t-dcl t-since-c99">
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<td>
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<div><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a> ctanhl<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a> z <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(3)</td>
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<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
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</tr>
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<tr class="t-dsc-header">
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<td>
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<div>定义于头文件 <code><tgmath.h></code></div>
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</td>
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<td></td>
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<td></td>
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</tr>
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<tr class="t-dcl t-since-c99">
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<td>
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<div><span class="mw-geshi c source-c"><span class="co2">#define tanh( z )</span></span></div>
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</td>
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<td>(4)</td>
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<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
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</tr>
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<tr class="t-dcl-sep">
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<td></td>
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<td></td>
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<td></td>
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</tr>
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</tbody>
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</table>
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<div class="t-li1"><span class="t-li">1-3)</span> 计算 <code>z</code> 的复双曲正切。</div>
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<div class="t-li1"><span class="t-li">4)</span> 泛型宏：若 <code>z</code> 拥有 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a></span></span> 类型，则调用 <code>ctanhl</code> 。若 <code>z</code> 拥有 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a></span></span> 类型，则调用 <code>ctanh</code> 。若 <code>z</code> 拥有 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">float</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a></span></span> 类型，则调用 <code>ctanhf</code> 。若 <code>z</code> 为实数或整数，则宏调用对应的实函数（ <span class="t-c"><span class="mw-geshi c source-c">tanhf</span></span> 、 <span class="t-c"><span class="mw-geshi c source-c"><a href="c-numeric-math-tanh.html"><span class="kw678">tanh</span></a></span></span> 、 <span class="t-c"><span class="mw-geshi c source-c">tanhl</span></span> ）。若 <code>z</code> 为虚数，则宏调用函数 <span class="t-lc"><a href="c-numeric-math-tan.html">tan</a></span> 的对应实数版本，实现公式 <span class="texhtml" style="white-space: nowrap;">tanh(iy) = i tan(y)</span> ，而返回类型为虚数。</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>z</td>
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<td>-</td>
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<td>复参数</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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<p>若不出现错误，则返回 <code>z</code> 的复双曲正切。</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="c-numeric-math-math_errhandling.html">math_errhandling</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 c source-c">ctanh<span class="br0">(</span><a href="c-numeric-complex-conj.html"><span class="kw760">conj</span></a><span class="br0">(</span>z<span class="br0">)</span><span class="br0">)</span> <span class="sy1">==</span> <a href="c-numeric-complex-conj.html"><span class="kw760">conj</span></a><span class="br0">(</span>ctanh<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 c source-c">ctanh<span class="br0">(</span><span class="sy2">-</span>z<span class="br0">)</span> <span class="sy1">==</span> <span class="sy2">-</span>ctanh<span class="br0">(</span>z<span class="br0">)</span></span></span></li>
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<li>若 <code>z</code> 为 <code>+0+0i</code> ，则结果为 <code>+0+0i</code></li>
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<li>若 <code>z</code> 为 <code>x+∞i</code> （对于任何<sup id="cite_ref-1" class="reference"><a href="c-numeric-complex-ctanh.html#cite_note-1">[1]</a></sup>有限 x ），结果为 <code>NaN+NaNi</code> 并引发 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span></li>
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<li>若 <code>z</code> 为 <code>x+NaN</code> （对于任何<sup id="cite_ref-2" class="reference"><a href="c-numeric-complex-ctanh.html#cite_note-2">[2]</a></sup>有限 x ），则结果为 <code>NaN+NaNi</code> 并可能引发 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span> 。</li>
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<li>若 <code>z</code> 为 <code>+∞+yi</code> （对于任何有限正 y ），则结果为 <code>1+0i</code></li>
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<li>若 <code>z</code> 为 <code>+∞+∞i</code> ，则结果为 <code>1±0i</code> （虚部符号未指定）</li>
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<li>若 <code>z</code> 为 <code>+∞+NaNi</code> ，则结果为 <code>1±0i</code> （虚部符号未指定）</li>
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<li>若 <code>z</code> 为 <code>NaN+0i</code> ，则结果为 <code>NaN+0i</code></li>
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<li>若 <code>z</code> 为 <code>NaN+yi</code> （对于任何非零 y ），则结果为 <code>NaN+NaNi</code> 并可能引发 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span> 。</li>
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<li>若 <code>z</code> 为 <code>NaN+NaNi</code> ，则结果为 <code>NaN+NaNi</code> 。</li>
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</ul>
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<ol class="references">
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<li id="cite_note-1"><span class="mw-cite-backlink"><a href="c-numeric-complex-ctanh.html#cite_ref-1">↑</a></span> <span class="reference-text">由 <a rel="nofollow" class="external text" href="http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1892.htm#dr_471">DR471</a> ，这只对非零 x 成立。若 <code>z</code> 为 <code>0+∞i</code> ，则结果应为 <code>0+NaNi</code> 。</span></li>
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<li id="cite_note-2"><span class="mw-cite-backlink"><a href="c-numeric-complex-ctanh.html#cite_ref-2">↑</a></span> <span class="reference-text">由 <a rel="nofollow" class="external text" href="http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1892.htm#dr_471">DR471</a> ，这只对非零 x 成立。若 <code>z</code> 为 <code>0+NaNi</code> ，则结果应为 <code>0+NaNi</code> 。</span></li>
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</ol>
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<h3><span class="mw-headline" id=".E6.B3.A8.E6.84.8F">注意</span></h3>
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双曲正切的数学定义是 <span class="texhtml" style="white-space: nowrap;">tanh z = <span class="t-mfrac"></span></span>
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<table>
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<tr>
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<td>e<span class="t-su">z<br /></span>-e<span class="t-su">-z<br /></span></td>
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</tr>
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<tr>
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<td>e<span class="t-su">z<br /></span>+e<span class="t-su">-z<br /></span></td>
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</tr>
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</table>
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。
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<p>双曲正切是复平面上的解析函数且无分支切割。它对于虚部是周期的，周期为 πi ，而且沿虚轴有一阶极点，位于坐标 <span class="texhtml" style="white-space: nowrap;">(0, π(1/2 + n))</span> 。然而无常用浮点表示能准确表示 π/2 ，故没有参数值能导致极点错误。</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="c source-c">
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<pre class="de1"><span class="co2">#include <stdio.h></span>
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<span class="co2">#include <math.h></span>
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<span class="co2">#include <complex.h></span>
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<span class="kw4">int</span> main<span class="br0">(</span><span class="kw4">void</span><span class="br0">)</span>
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<span class="br0">{</span>
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<span class="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a> z <span class="sy1">=</span> ctanh<span class="br0">(</span><span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 表现类似沿实轴的 tanh</span>
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<a href="c-io-fprintf.html"><span class="kw848">printf</span></a><span class="br0">(</span><span class="st0">"tanh(1+0i) = %f%+fi (tanh(1)=%f)<span class="es1">\n</span>"</span>, <a href="c-numeric-complex-creal.html"><span class="kw754">creal</span></a><span class="br0">(</span>z<span class="br0">)</span>, <a href="c-numeric-complex-cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span>z<span class="br0">)</span>, <a href="c-numeric-math-tanh.html"><span class="kw678">tanh</span></a><span class="br0">(</span><span class="nu0">1</span><span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a> z2 <span class="sy1">=</span> ctanh<span class="br0">(</span>I<span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 表现类似沿虚轴的正切</span>
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<a href="c-io-fprintf.html"><span class="kw848">printf</span></a><span class="br0">(</span><span class="st0">"tanh(0+1i) = %f%+fi ( tan(1)=%f)<span class="es1">\n</span>"</span>, <a href="c-numeric-complex-creal.html"><span class="kw754">creal</span></a><span class="br0">(</span>z2<span class="br0">)</span>, <a href="c-numeric-complex-cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span>z2<span class="br0">)</span>, <a href="c-numeric-math-tan.html"><span class="kw671">tan</span></a><span class="br0">(</span><span class="nu0">1</span><span class="br0">)</span><span class="br0">)</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">tanh(1+0i) = 0.761594+0.000000i (tanh(1)=0.761594)
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tanh(0+1i) = 0.000000+1.557408i ( tan(1)=1.557408)</pre></div>
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</div>
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</div>
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<h3><span class="mw-headline" id=".E5.BC.95.E7.94.A8">引用</span></h3>
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<div class="t-ref-std-11">
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<ul>
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<li>C11 标准（ISO/IEC 9899:2011）：</li>
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</ul>
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<dl>
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<dd>
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<ul>
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<li>7.3.6.6 The ctanh functions (p: 194)</li>
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</ul>
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</dd>
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</dl>
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<dl>
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<dd>
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<ul>
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<li>7.25 Type-generic math <tgmath.h> (p: 373-375)</li>
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</ul>
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</dd>
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</dl>
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<dl>
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<dd>
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<ul>
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<li>G.6.2.6 The ctanh functions (p: 542)</li>
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</ul>
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</dd>
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</dl>
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<dl>
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<dd>
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<ul>
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<li>G.7 Type-generic math <tgmath.h> (p: 545)</li>
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</ul>
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</dd>
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</dl>
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<div class="t-ref-std-c99">
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<ul>
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<li>C99 标准（ISO/IEC 9899:1999）：</li>
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</ul>
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<dl>
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<dd>
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<ul>
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<li>7.3.6.6 The ctanh functions (p: 176)</li>
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</ul>
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</dd>
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</dl>
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<dl>
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<dd>
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<ul>
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<li>7.22 Type-generic math <tgmath.h> (p: 335-337)</li>
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</ul>
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</dd>
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</dl>
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<dl>
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<dd>
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<ul>
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<li>G.6.2.6 The ctanh functions (p: 477)</li>
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</ul>
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</dd>
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</dl>
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<dl>
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<dd>
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<ul>
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<li>G.7 Type-generic math <tgmath.h> (p: 480)</li>
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</ul>
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</dd>
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</dl>
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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="c-numeric-complex-csinh.html"><span class="t-lines"><span>csinh</span><span>csinhf</span><span>csinhl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算复数双曲正弦<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="c-numeric-complex-ccosh.html"><span class="t-lines"><span>ccosh</span><span>ccoshf</span><span>ccoshl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算复双曲余弦<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="c-numeric-complex-catanh.html"><span class="t-lines"><span>catanh</span><span>catanhf</span><span>catanhl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算复数反双曲正切<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="c-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-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</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>
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</table>
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</div>
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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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