168 lines
15 KiB
HTML
168 lines
15 KiB
HTML
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<title>std::log(std::complex)</title>
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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>log<span style="font-size:0.7em; line-height:130%">(std::complex)</span></h1>
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<div id="contentSub"><span class="subpages">< <a href="cpp.html">cpp</a>‎ | <a href="cpp-numeric.html">numeric</a>‎ | <a href="cpp-numeric-complex.html">complex</a></span></div>
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<div>定义于头文件 <code><a href="cpp-header-complex.html"><complex></a></code></div>
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<td></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw1">template</span><span class="sy1"><</span> <span class="kw1">class</span> T <span class="sy1">></span><br />
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complex<span class="sy1"><</span>T<span class="sy1">></span> log<span class="br0">(</span> <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span> z <span class="br0">)</span><span class="sy4">;</span></span></div>
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<td class="t-dcl-nopad"></td>
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<td></td>
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<td></td>
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</table>
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<p>计算 <code>z</code> 的复自然（底 <i>e</i> ）对数，分支切割沿负实轴。</p>
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<h3><span class="mw-headline" id=".E5.8F.82.E6.95.B0">参数</span></h3>
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<table class="t-par-begin">
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<td>z</td>
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<td>-</td>
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<td>复数值</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="cpp-numeric-math-math_errhandling.html"><tt>math_errhandling</tt></a> 一致。</p>
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<p>若实现支持 IEEE 浮点算术，则</p>
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<ul>
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<li>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 cpp source-cpp"><a href="cpp-numeric-math-log.html"><span class="kw1324">std::<span class="me2">log</span></span></a><span class="br0">(</span>std<span class="sy4">::</span><span class="me2">conj</span><span class="br0">(</span>z<span class="br0">)</span><span class="br0">)</span> <span class="sy1">==</span> std<span class="sy4">::</span><span class="me2">conj</span><span class="br0">(</span><a href="cpp-numeric-math-log.html"><span class="kw1324">std::<span class="me2">log</span></span></a><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,+0)</code> ，则结果为 <code>(-∞,π)</code> 并引发 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_DIVBYZERO</a></span></li>
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<li>若 <code>z</code> 为 <code>(+0,+0)</code> ，则结果为 <code>(-∞,+0)</code> 并引发 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_DIVBYZERO</a></span></li>
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<li>若 <code>z</code> 为 <code>(x,+∞)</code> （对于任何有限 x ），则结果为 <code>(+∞,π/2)</code></li>
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<li>若 <code>z</code> 为 <code>(x,NaN)</code> （对于任何有限 x ），则结果为 <code>(NaN,NaN)</code> 并可能引发 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span></li>
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<li>若 <code>z</code> 为 <code>(-∞,y)</code> （对于任何有限正 y ），则结果为 <code>(+∞,π)</code></li>
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<li>若 <code>z</code> 为 <code>(+∞,y)</code> （对于任何有限正 y ），则结果为 <code>(+∞,+0)</code></li>
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<li>若 <code>z</code> 为 <code>(-∞,+∞)</code> ，则结果为 <code>(+∞,3π/4)</code></li>
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<li>若 <code>z</code> 为 <code>(+∞,+∞)</code> ，则结果为 <code>(+∞,π/4)</code></li>
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<li>若 <code>z</code> 为 <code>(±∞,NaN)</code>，则结果为 <code>(+∞,NaN)</code></li>
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<li>若 <code>z</code> 为 <code>(NaN,y)</code> （对于任何有限 y ），则结果为 <code>(NaN,NaN)</code> 并可能引发 <span class="t-lc"><a href="cpp-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span></li>
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<li>若 <code>z</code> 为 <code>(NaN,+∞)</code> ，则结果为 <code>(+∞,NaN)</code></li>
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<li>若 <code>z</code> 为 <code>(NaN,NaN)</code> ，则结果为 <code>(NaN,NaN)</code></li>
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</ul>
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<h3><span class="mw-headline" id=".E6.B3.A8.E6.84.8F">注意</span></h3>
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<p>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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<p>此函数语义的目的是与 C 函数 <a href="c-numeric-complex-clog.html"><tt>clog</tt></a> 一致。</p>
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<h3><span class="mw-headline" id=".E7.BC.BA.E9.99.B7.E6.8A.A5.E5.91.8A">缺陷报告</span></h3>
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<p>下列更改行为的缺陷报告追溯地应用于以前出版的 C++ 标准。</p>
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<table class="dsctable" style="font-size:0.8em">
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<tr>
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<th>DR</th>
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<th>应用于</th>
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<th>出版时的行为</th>
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<th>正确行为</th>
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<tr>
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<td><a rel="nofollow" class="external text" href="https://cplusplus.github.io/LWG/issue2597">LWG 2597</a></td>
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<td>C++98</td>
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<td>规定错误地处理了有符号零虚部</td>
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<td>移除错误的要求</td>
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</tr>
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</table>
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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 class="cpp source-cpp">
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<pre class="de1"><span class="co2">#include <iostream></span>
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<span class="co2">#include <cmath></span>
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<span class="co2">#include <complex></span>
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<span class="kw4">int</span> main<span class="br0">(</span><span class="br0">)</span>
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<span class="br0">{</span>
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<a href="cpp-numeric-complex.html"><span class="kw1472">std::<span class="me2">complex</span></span></a><span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span> z<span class="br0">(</span><span class="nu0">0</span>, <span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// // r = 1, θ = pi/2</span>
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<a href="cpp-io-cout.html"><span class="kw1758">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"2*log"</span> <span class="sy1"><<</span> z <span class="sy1"><<</span> <span class="st0">" = "</span> <span class="sy1"><<</span> <span class="nu0">2</span>.<span class="sy2">*</span><a href="cpp-numeric-math-log.html"><span class="kw1324">std::<span class="me2">log</span></span></a><span class="br0">(</span>z<span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
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<a href="cpp-numeric-complex.html"><span class="kw1472">std::<span class="me2">complex</span></span></a><span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span> z2<span class="br0">(</span>sqrt<span class="br0">(</span><span class="nu0">2</span><span class="br0">)</span><span class="sy2">/</span><span class="nu0">2</span>, sqrt<span class="br0">(</span><span class="nu0">2</span><span class="br0">)</span><span class="sy2">/</span><span class="nu0">2</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// r = 1, θ = pi/4</span>
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<a href="cpp-io-cout.html"><span class="kw1758">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"4*log"</span> <span class="sy1"><<</span> z2 <span class="sy1"><<</span> <span class="st0">" = "</span> <span class="sy1"><<</span> <span class="nu0">4</span>.<span class="sy2">*</span><a href="cpp-numeric-math-log.html"><span class="kw1324">std::<span class="me2">log</span></span></a><span class="br0">(</span>z2<span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
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<a href="cpp-numeric-complex.html"><span class="kw1472">std::<span class="me2">complex</span></span></a><span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span> z3<span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span>, <span class="nu0">0</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// r = 1, θ = pi</span>
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<a href="cpp-io-cout.html"><span class="kw1758">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"log"</span> <span class="sy1"><<</span> z3 <span class="sy1"><<</span> <span class="st0">" = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-math-log.html"><span class="kw1324">std::<span class="me2">log</span></span></a><span class="br0">(</span>z3<span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
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<a href="cpp-numeric-complex.html"><span class="kw1472">std::<span class="me2">complex</span></span></a><span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span> z4<span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span>, <span class="sy2">-</span><span class="nu16">0.0</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 分支的另一侧</span>
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<a href="cpp-io-cout.html"><span class="kw1758">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"log"</span> <span class="sy1"><<</span> z4 <span class="sy1"><<</span> <span class="st0">" (the other side of the cut) = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-math-log.html"><span class="kw1324">std::<span class="me2">log</span></span></a><span class="br0">(</span>z4<span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
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<span class="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(0,1) = (0,3.14159)
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4*log(0.707107,0.707107) = (0,3.14159)
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log(-1,0) = (0,3.14159)
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log(-1,-0) (the other side of the cut) = (0,-3.14159)</pre></div>
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<h3><span class="mw-headline" id=".E5.8F.82.E9.98.85">参阅</span></h3>
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<table class="t-dsc-begin">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-log10.html"><span class="t-lines"><span>log10<span class="t-dsc-small">(std::complex)</span></span></span></a></div>
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</div>
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</td>
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<td>沿负实轴分割的复常用对数<br />
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<span class="t-mark">(函数模板)</span></td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-complex-exp.html"><span class="t-lines"><span>exp<span class="t-dsc-small">(std::complex)</span></span></span></a></div>
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</div>
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</td>
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<td>以 <i>e</i> 为底复数的指数<br />
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<span class="t-mark">(函数模板)</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="cpp-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-cxx11">(C++11)</span></span><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
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</div>
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<td>计算自然（以 <i>e</i> 为底）对数（ <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 class="t-dsc">
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-valarray-log.html"><span class="t-lines"><span>log<span class="t-dsc-small">(std::valarray)</span></span></span></a></div>
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</div>
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</td>
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<td>应用函数 <span class="t-lc"><a href="cpp-numeric-math-log.html">std::log</a></span> 到 valarray 的每个元素<br />
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<span class="t-mark">(函数模板)</span></td>
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