222 lines
14 KiB
HTML
222 lines
14 KiB
HTML
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<title>cexpf, cexp, cexpl</title>
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<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-c_numeric_complex_cexp skin-cppreference2 action-view cpp-navbar">
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<h1 id="firstHeading" class="firstHeading">cexpf, cexp, cexpl</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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<div>定义于头文件 <code><complex.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="kw4">float</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a> cexpf<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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<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> cexp<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> cexpl<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 class="t-dsc-header">
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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 exp( 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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<div class="t-li1"><span class="t-li">1-3)</span> 计算复数的 <code>z</code> 的底 <i>e</i> 指数。</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>cexpl</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>cexp</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>cexpf</code> 。若 <code>z</code> 是实浮点数或整数，则该宏调用对应的实函数（ <span class="t-c"><span class="mw-geshi c source-c">expf</span></span> 、 <span class="t-c"><span class="mw-geshi c source-c"><a href="c-numeric-math-exp.html"><span class="kw657">exp</span></a></span></span> 、 <span class="t-c"><span class="mw-geshi c source-c">expl</span></span> ）。若 <code>z</code> 是虚数，则调用对应的复参数版本。</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 <i>e</i> 的 <code>z</code> 次幂， <span class="texhtml" style="white-space: nowrap;">e<span class="t-su">z<br /></span></span> 。</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">cexp<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>cexp<span class="br0">(</span>z<span class="br0">)</span><span class="br0">)</span></span></span></li>
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<li>若 <code>z</code> 为 <code>±0+0i</code> ，则结果是<code>1+0i</code>；</li>
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<li>若 <code>z</code> 为 <code>x+∞i</code> （对于任何有限 x），则结果是 <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+NaNi</code> （对于任何有限 x），则结果是 <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>+∞+0i</code> ，则结果是<code>+∞+0i</code>；</li>
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<li>若 <code>z</code> 为 <code>-∞+yi</code> （对任何有限 y），则结果是 <code>+0cis(y)</code> ；</li>
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<li>若 <code>z</code> 为 <code>+∞+yi</code> （对于任何有限非零 y），则结果是 <code>+∞cis(y)</code> ；</li>
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<li>若 <code>z</code> 为 <code>-∞+∞i</code> ，则结果是 <code>±0±0i</code> （符号未指定）</li>
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<li>若 <code>z</code> 为 <code>+∞+∞i</code> ，则结果是 <code>±∞+NaNi</code> 并引发 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span> （实部符号未指定）；</li>
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<li>若 <code>z</code> 为 <code>-∞+NaNi</code> ，则结果是 <code>±0±0i</code> （符号未指定）；</li>
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<li>若 <code>z</code> 为 <code>+∞+NaNi</code> ，则结果是 <code>±∞+NaNi</code> （实部符号未指定）；</li>
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<li>若 <code>z</code> 为 <code>NaN+0i</code> ，则结果是 <code>NaN+0i</code> ；</li>
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<li>若 <code>z</code> 为 <code>NaN+yi</code> （对于任意非零 y ），则结果是 <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> ，则结果是 <code>NaN+NaNi</code> ；</li>
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</ul>
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<p>其中 <span class="texhtml" style="white-space: nowrap;">cis(y)</span> 为 <span class="texhtml" style="white-space: nowrap;">cos(y) + i sin(y)</span> 。</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>复指数函数 <span class="texhtml" style="white-space: nowrap;">e<span class="t-su">z<br /></span></span> 对于自变量 <span class="texhtml" style="white-space: nowrap;">z = x+iy</span> 的值等于 <span class="texhtml" style="white-space: nowrap;">e<span class="t-su">x<br /></span> cis(y)</span> ，或 <span class="texhtml" style="white-space: nowrap;">e<span class="t-su">x<br /></span> (cos(y) + i sin(y))</span> 。</p>
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<p>指数函数在复平面上是<i>整函数</i>且无分支切割。</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> PI <span class="sy1">=</span> <a href="c-numeric-math-acos.html"><span class="kw673">acos</span></a><span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</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> z <span class="sy1">=</span> cexp<span class="br0">(</span>I <span class="sy2">*</span> PI<span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 欧拉公式</span>
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<a href="c-io-fprintf.html"><span class="kw848">printf</span></a><span class="br0">(</span><span class="st0">"exp(i*pi) = %.1f%+.1fi<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><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">exp(i*pi) = -1.0+0.0i</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>7.3.7.1 The cexp 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.6.3.1 The cexp functions (p: 543)</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>7.3.7.1 The cexp 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.6.3.1 The cexp functions (p: 478)</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-clog.html"><span class="t-lines"><span>clog</span><span>clogf</span><span>clogl</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>计算复数的自然对数<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-math-exp.html"><span class="t-lines"><span>exp</span><span>expf</span><span>expl</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 <i>e</i> 的给定次幂 （ <span class="mjax" style="display:none">\({\small e^x}\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">e<sup>x</sup></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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