230 lines
14 KiB
HTML
230 lines
14 KiB
HTML
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<title>ctanf, ctan, ctanl</title>
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<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-c_numeric_complex_ctan skin-cppreference2 action-view cpp-navbar">
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<h1 id="firstHeading" class="firstHeading">ctanf, ctan, ctanl</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>定义于头文件 <code><complex.h></code></div>
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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> ctanf<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>(1)</td>
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<td><span class="t-mark-rev t-since-c99">(C99 起)</span></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> ctan<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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<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> ctanl<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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<div>定义于头文件 <code><tgmath.h></code></div>
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<td></td>
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<td></td>
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<div><span class="mw-geshi c source-c"><span class="co2">#define tan( z )</span></span></div>
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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 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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<div class="t-li1"><span class="t-li">1-3)</span> 计算 <code>z</code> 的复正切。</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>ctanl</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>ctan</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>ctanf</code> 。若 <code>z</code> 为实数或整数，则该宏调用对应的实函数（ <span class="t-c"><span class="mw-geshi c source-c">tanf</span></span> 、 <span class="t-c"><span class="mw-geshi c source-c"><a href="c-numeric-math-tan.html"><span class="kw671">tan</span></a></span></span> 、 <span class="t-c"><span class="mw-geshi c source-c">tanl</span></span> ）。若 <code>z</code> 为虚数，则该宏调用函数 <span class="t-lc"><a href="c-numeric-math-tanh.html">tanh</a></span> 的对应实版本，实现公式 <span class="texhtml" style="white-space: nowrap;">tan(iy) = i tanh(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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<td>z</td>
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<td>-</td>
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<td>复参数</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>若无错误发生，则返回 <code>z</code> 的复正切。</p>
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<p>错误和特殊情况如同运算实现为 <span class="t-c"><span class="mw-geshi c source-c"><span class="sy2">-</span>i <span class="sy2">*</span> <a href="c-numeric-complex-ctanh.html"><span class="kw811">ctanh</span></a><span class="br0">(</span>i<span class="sy2">*</span>z<span class="br0">)</span></span></span> 一般处理，其中 <code>i</code> 是虚数单位。</p>
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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>正切是复平面上的解析函数，而无分支切割。它对于实部是周期的，周期为 πi ，而且沿实轴有一阶极点，位于坐标 <span class="texhtml" style="white-space: nowrap;">(π(1/2 + n), 0)</span> 。然而无常用浮点表示能准确表示 π/2 ，故而没有值使得极点错误出现。</p>
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正切的数学定义是 <span class="texhtml" style="white-space: nowrap;">tan z = <span class="t-mfrac"></span></span>
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<table>
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<td>i(e<span class="t-su">-iz<br /></span>-e<span class="t-su">iz<br /></span>)</td>
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<td>e<span class="t-su">-iz<br /></span>+e<span class="t-su">iz<br /></span></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="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> ctan<span class="br0">(</span><span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 表现类似沿实轴的实正切</span>
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<a href="c-io-fprintf.html"><span class="kw848">printf</span></a><span class="br0">(</span><span class="st0">"tan(1+0i) = %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>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-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="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a> z2 <span class="sy1">=</span> ctan<span class="br0">(</span>I<span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 表现类似沿虚轴的 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">"tan(0+1i) = %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>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-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="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">tan(1+0i) = 1.557408+0.000000i ( tan(1)=1.557408)
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tan(0+1i) = 0.000000+0.761594i (tanh(1)=0.761594)</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>7.3.5.6 The ctan functions (p: 192)</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 complex <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.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>7.3.5.6 The ctan functions (p: 174)</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 complex <tgcomplex.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.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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<div class="t-dsc-member-div">
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<div><a href="c-numeric-complex-ctanh.html"><span class="t-lines"><span>ctanh</span><span>ctanhf</span><span>ctanhl</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>计算复数双曲正切<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="c-numeric-complex-csin.html"><span class="t-lines"><span>csin</span><span>csinf</span><span>csinl</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-ccos.html"><span class="t-lines"><span>ccos</span><span>ccosf</span><span>ccosl</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>计算复数余弦<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="c-numeric-complex-catan.html"><span class="t-lines"><span>catan</span><span>catanf</span><span>catanl</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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<div class="t-dsc-member-div">
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<div><a href="c-numeric-math-tan.html"><span class="t-lines"><span>tan</span><span>tanf</span><span>tanl</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>计算正切（ <span class="mjax" style="display:none">\({\small\tan{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">tan(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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</body>
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