258 lines
17 KiB
HTML
258 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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<title>cacosf, cacos, cacosl</title>
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<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-c_numeric_complex_cacos 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">cacosf, cacos, cacosl</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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<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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<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> cacosf<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 class="t-dcl t-since-c99">
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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> cacos<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> cacosl<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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<div><span class="mw-geshi c source-c"><span class="co2">#define acos( 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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<div class="t-li1"><span class="t-li">1-3)</span> 计算 <code>z</code> 的复弧（反）余弦，分支切割在沿实轴的区间 <span class="texhtml" style="white-space: nowrap;">[−1,+1]</span> 外。</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>cacosl</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>cacos</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>cacosf</code> 。若 <code>z</code> 为实数或整数，则宏调用对应的实数函数（ <span class="t-c"><span class="mw-geshi c source-c">acosf</span></span> 、 <span class="t-c"><span class="mw-geshi c source-c"><a href="c-numeric-math-acos.html"><span class="kw673">acos</span></a></span></span> 、 <span class="t-c"><span class="mw-geshi c source-c">acosl</span></span> ）。若 <code>z</code> 为虚数，则宏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>若不出现错误，则返回 <code>z</code> 的复弧（反）余弦，于沿实轴的范围 <span class="texhtml" style="white-space: nowrap;">[0 ; ∞)</span> 且于沿虚轴的范围 <span class="texhtml" style="white-space: nowrap;">[−<i>i</i>π ; <i>i</i>π]</span> 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"><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><span class="t-c"><span class="mw-geshi c source-c">cacos<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>cacos<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>π/2-0i</code></li>
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<li>若 <code>z</code> 为 <code>±0+NaNi</code> ，则结果为 <code>π/2+NaNi</code></li>
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<li>若 <code>z</code> 为 <code>x+∞i</code> （对于任何有限 x ），则结果为 <code>π/2-∞i</code></li>
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<li>若 <code>z</code> 为 <code>x+NaNi</code> （对于任何有限非零 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>π-∞i</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>+0-∞i</code></li>
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<li>若 <code>z</code> 为 <code>-∞+∞i</code> ，则结果为 <code>3π/4-∞i</code></li>
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<li>若 <code>z</code> 为 <code>+∞+∞i</code> ，则结果为 <code>π/4-∞i</code></li>
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<li>若 <code>z</code> 为 <code>±∞+NaNi</code> ，则结果为 <code>NaN±∞i</code> （虚部符号未指定）</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>NaN-∞i</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.E8.A7.A3">注解</span></h3>
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<p>反余弦（或弧余弦）是多值函数，要求复平面上的分支切割。约定将分支切割置于实轴的线段 <span class="texhtml" style="white-space: nowrap;">(-∞,-1)</span> 和 <span class="texhtml" style="white-space: nowrap;">(1,∞)</span> 上。</p>
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弧（反）余弦主值的数学定义是 <span class="texhtml" style="white-space: nowrap;">acos z = <span class="t-mfrac"></span></span>
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<table>
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<tr>
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<td>1</td>
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</tr>
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<tr>
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<td>2</td>
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</tr>
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</table>
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π + <i>i</i>ln(<i>i</i>z + <span class="t-mrad"><span>√</span><span>1-z<span class="t-su">2<br /></span></span></span>) 。
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<p>对于任何 z ， <span class="texhtml" style="white-space: nowrap;">acos(z) = π - acos(-z)</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> cacos<span class="br0">(</span><span class="sy2">-</span><span class="nu0">2</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="c-io-fprintf.html"><span class="kw848">printf</span></a><span class="br0">(</span><span class="st0">"cacos(-2+0i) = %f%+fi<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="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a> z2 <span class="sy1">=</span> cacos<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">2</span><span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 或 CMPLX(-2, -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">"cacos(-2-0i) (the other side of the cut) = %f%+fi<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><span class="br0">)</span><span class="sy4">;</span>
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<span class="co1">// 对于任何 z ， acos(z) = pi - acos(-z)</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> z3 <span class="sy1">=</span> <a href="c-numeric-complex-ccos.html"><span class="kw787">ccos</span></a><span class="br0">(</span>pi<span class="sy2">-</span>z2<span class="br0">)</span><span class="sy4">;</span>
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<a href="c-io-fprintf.html"><span class="kw848">printf</span></a><span class="br0">(</span><span class="st0">"ccos(pi - cacos(-2-0i) = %f%+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="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">cacos(-2+0i) = 3.141593-1.316958i
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cacos(-2-0i) (the other side of the cut) = 3.141593+1.316958i
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ccos(pi - cacos(-2-0i) = 2.000000+0.000000i</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>7.3.5.1 The cacos functions (p: 190)</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.6.1.1 The cacos functions (p: 539)</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>7.3.5.1 The cacos functions (p: 172)</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.6.1.1 The cacos functions (p: 474)</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-casin.html"><span class="t-lines"><span>casin</span><span>casinf</span><span>casinl</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-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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<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>
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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-acos.html"><span class="t-lines"><span>acos</span><span>acosf</span><span>acosl</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>计算反余弦（ <span class="mjax" style="display:none">\({\small\arccos{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arccos(x)</span> ）<br />
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<span class="t-mark">(函数)</span></td>
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