230 lines
17 KiB
HTML
230 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>clogf, clog, clogl</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_clog 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">clogf, clog, clogl</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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<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 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> clogf<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> clog<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> clogl<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 log( 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> 的复自然（底 <i>e</i> ）对数，分支切割沿负实轴。</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>clogl</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>clog</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>clogf</code> 。若 <code>z</code> 为实数或整数，则该宏调用对应的实数函数（ <span class="t-c"><span class="mw-geshi c source-c">logf</span></span> 、 <span class="t-c"><span class="mw-geshi c source-c"><a href="c-numeric-math-log.html"><span class="kw660">log</span></a></span></span> 、 <span class="t-c"><span class="mw-geshi c source-c">logl</span></span> ）。若 <code>z</code> 为虚数，则调用对应的复数版本。</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>若不发生错误，则返回 <code>z</code> 的复自然对数，在沿虚轴为区间 <span class="texhtml" style="white-space: nowrap;">[−iπ, +iπ]</span> ，沿实轴为数学上无界的条状范围中。</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="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>考虑虚部符号，函数连续到分支切割上</li>
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<li><span class="t-c"><span class="mw-geshi c source-c">clog<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>clog<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> ，则结果为 <code>-∞+πi</code> 并引发 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_DIVBYZERO</a></span></li>
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<li>若 <code>z</code> 为 <code>+0+0i</code> ，则结果为 <code>-∞+0i</code> 并引发 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_DIVBYZERO</a></span></li>
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<li>若 <code>z</code> 为 <code>x+∞i</code> （对于任何有限 x ），则结果为 <code>+∞+πi/2</code></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>+∞+πi</code></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>+∞+0i</code></li>
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<li>若 <code>z</code> 为 <code>-∞+∞i</code> ，则结果为 <code>+∞+3πi/4</code></li>
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<li>若 <code>z</code> 为 <code>+∞+∞i</code> ，则结果为 <code>+∞+πi/4</code></li>
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<li>若 <code>z</code> 为 <code>±∞+NaNi</code> ，则结果为 <code>+∞+NaNi</code></li>
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<li>若 <code>z</code> 为 <code>NaN+yi</code> （对于任何有限 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+∞i</code> ，则结果为 <code>+∞+NaNi</code></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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<h3><span class="mw-headline" id=".E6.B3.A8.E6.84.8F">注意</span></h3>
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<p>拥有极坐标表示 <span class="texhtml" style="white-space: nowrap;">(r,θ)</span> 的复数 <span class="texhtml" style="white-space: nowrap;">z</span> 的自然对数等于 <span class="texhtml" style="white-space: nowrap;">ln r + i(θ+2nπ)</span> ，其主值为 <span class="texhtml" style="white-space: nowrap;">ln r + iθ</span> 。</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> clog<span class="br0">(</span>I<span class="br0">)</span><span class="sy4">;</span> <span class="co1">// r = 1, θ = pi/2</span>
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<a href="c-io-fprintf.html"><span class="kw848">printf</span></a><span class="br0">(</span><span class="st0">"2*log(i) = %.1f%+fi<span class="es1">\n</span>"</span>, <a href="c-numeric-complex-creal.html"><span class="kw754">creal</span></a><span class="br0">(</span><span class="nu0">2</span><span class="sy2">*</span>z<span class="br0">)</span>, <a href="c-numeric-complex-cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span><span class="nu0">2</span><span class="sy2">*</span>z<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> clog<span class="br0">(</span><a href="c-numeric-math-sqrt.html"><span class="kw665">sqrt</span></a><span class="br0">(</span><span class="nu0">2</span><span class="br0">)</span><span class="sy2">/</span><span class="nu0">2</span> <span class="sy2">+</span> <a href="c-numeric-math-sqrt.html"><span class="kw665">sqrt</span></a><span class="br0">(</span><span class="nu0">2</span><span class="br0">)</span><span class="sy2">/</span><span class="nu0">2</span><span class="sy2">*</span>I<span class="br0">)</span><span class="sy4">;</span> <span class="co1">// r = 1, θ = pi/4</span>
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<a href="c-io-fprintf.html"><span class="kw848">printf</span></a><span class="br0">(</span><span class="st0">"4*log(sqrt(2)/2+sqrt(2)i/2) = %.1f%+fi<span class="es1">\n</span>"</span>, <a href="c-numeric-complex-creal.html"><span class="kw754">creal</span></a><span class="br0">(</span><span class="nu0">4</span><span class="sy2">*</span>z2<span class="br0">)</span>, <a href="c-numeric-complex-cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span><span class="nu0">4</span><span class="sy2">*</span>z2<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> z3 <span class="sy1">=</span> clog<span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// r = 1, θ = pi</span>
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<a href="c-io-fprintf.html"><span class="kw848">printf</span></a><span class="br0">(</span><span class="st0">"log(-1+0i) = %.1f%+fi<span class="es1">\n</span>"</span>, <a href="c-numeric-complex-creal.html"><span class="kw754">creal</span></a><span class="br0">(</span>z3<span class="br0">)</span>, <a href="c-numeric-complex-cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span>z3<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> z4 <span class="sy1">=</span> clog<span class="br0">(</span><a href="c-numeric-complex-conj.html"><span class="kw760">conj</span></a><span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span><span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 或 C11 中的 clog(CMPLX(-1, -0.0))</span>
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<a href="c-io-fprintf.html"><span class="kw848">printf</span></a><span class="br0">(</span><span class="st0">"log(-1-0i) (the other side of the cut) = %.1f%+fi<span class="es1">\n</span>"</span>, <a href="c-numeric-complex-creal.html"><span class="kw754">creal</span></a><span class="br0">(</span>z4<span class="br0">)</span>, <a href="c-numeric-complex-cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span>z4<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">2*log(i) = 0.0+3.141593i
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4*log(sqrt(2)/2+sqrt(2)i/2) = 0.0+3.141593i
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log(-1+0i) = 0.0+3.141593i
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log(-1-0i) (the other side of the cut) = 0.0-3.141593i</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>7.3.7.2 The clog functions (p: 195)</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.6.3.2 The clog functions (p: 543-544)</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>7.3.7.2 The clog functions (p: 176-177)</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.6.3.2 The clog functions (p: 478-479)</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-cexp.html"><span class="t-lines"><span>cexp</span><span>cexpf</span><span>cexpl</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 e 底指数<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-log.html"><span class="t-lines"><span>log</span><span>logf</span><span>logl</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>计算自然对数（底为 <i>e</i> ）（ <span class="mjax" style="display:none">\({\small \ln{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">ln(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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