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<h1 id="firstHeading" class="firstHeading">catanf, catan, catanl</h1>
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<div id="contentSub"><span class="subpages">&lt; <a href="c.html">c</a>&lrm; | <a href="c-numeric.html">numeric</a>&lrm; | <a href="c-numeric-complex.html">complex</a></span></div>
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<div>&#23450;&#20041;&#20110;&#22836;&#25991;&#20214; <code>&lt;complex.h&gt;</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> &nbsp; &nbsp; &nbsp; catanf<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>
<td><span class="t-mark-rev t-since-c99">(C99 &#36215;)</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> &nbsp; &nbsp; &nbsp;catan<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>(2)</td>
<td><span class="t-mark-rev t-since-c99">(C99 &#36215;)</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> catanl<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>(3)</td>
<td><span class="t-mark-rev t-since-c99">(C99 &#36215;)</span></td>
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<div>&#23450;&#20041;&#20110;&#22836;&#25991;&#20214; <code>&lt;tgmath.h&gt;</code></div>
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<div><span class="mw-geshi c source-c"><span class="co2">#define atan( z )</span></span></div>
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<td>(4)</td>
<td><span class="t-mark-rev t-since-c99">(C99 &#36215;)</span></td>
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<div class="t-li1"><span class="t-li">1-3)</span> &#35745;&#31639; <code>z</code> &#30340;&#22797;&#24359;&#65288;&#21453;&#65289;&#27491;&#20999;&#65292;&#20998;&#25903;&#20999;&#21106;&#22312;&#27839;&#34394;&#36724;&#30340; <span class="texhtml" style="white-space: nowrap;">[&minus;i,+i]</span> &#21306;&#38388;&#22806;&#12290;</div>
<div class="t-li1"><span class="t-li">4)</span> &#27867;&#22411;&#23439;&#65306;&#33509; <code>z</code> &#25317;&#26377; <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> &#31867;&#22411;&#65292;&#21017;&#35843;&#29992; <code>catanl</code> &#12290;&#33509; <code>z</code> &#25317;&#26377; <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> &#31867;&#22411;&#65292;&#21017;&#35843;&#29992; <code>catan</code> &#12290;&#33509; <code>z</code> &#25317;&#26377; <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> &#31867;&#22411;&#65292;&#21017;&#35843;&#29992; <code>catanf</code> &#12290;&#33509; <code>z</code> &#20026;&#23454;&#25968;&#25110;&#25972;&#25968;&#65292;&#21017;&#23439;&#35843;&#29992;&#23545;&#24212;&#30340;&#23454;&#25968;&#20989;&#25968;&#65288; <span class="t-c"><span class="mw-geshi c source-c">atanf</span></span> &#12289; <span class="t-c"><span class="mw-geshi c source-c"><a href="c-numeric-math-atan.html"><span class="kw674">atan</span></a></span></span> &#12289; <span class="t-c"><span class="mw-geshi c source-c">atanl</span></span> &#65289;&#12290;&#33509; <code>z</code> &#20026;&#34394;&#25968;&#65292;&#21017;&#23439;&#35843;&#29992;&#20989;&#25968; <span class="t-lc"><a href="c-numeric-math-atanh.html">atanh</a></span> &#30340;&#23545;&#24212;&#23454;&#25968;&#29256;&#26412;&#65292;&#23454;&#29616;&#20844;&#24335; <span class="texhtml" style="white-space: nowrap;">atan(iy) = i atanh(y)</span> &#65292;&#32780;&#23439;&#30340;&#36820;&#22238;&#31867;&#22411;&#20026;&#34394;&#25968;&#12290;</div>
<h3><span class="mw-headline" id=".E5.8F.82.E6.95.B0">&#21442;&#25968;</span></h3>
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<td>z</td>
<td>-</td>
<td>&#22797;&#21442;&#25968;</td>
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<h3><span class="mw-headline" id=".E8.BF.94.E5.9B.9E.E5.80.BC">&#36820;&#22238;&#20540;</span></h3>
<p>&#33509;&#19981;&#21457;&#29983;&#38169;&#35823;&#65292;&#21017;&#36820;&#22238; <code>z</code> &#30340;&#22797;&#24359;&#65288;&#21453;&#65289;&#27491;&#20999;&#65292;&#22312;&#27839;&#34394;&#36724;&#26080;&#30028;&#65292;&#27839;&#23454;&#36724;&#22312;&#21306;&#38388; <span class="texhtml" style="white-space: nowrap;">[&minus;&pi;/2; +&pi;/2]</span> &#20869;&#30340;&#26465;&#29366;&#33539;&#22260;&#20013;&#12290;</p>
<p>&#25353;&#29031;&#22914;&#21516;&#20197; <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-catanh.html"><span class="kw802">catanh</span></a><span class="br0">(</span>I<span class="sy2">*</span>z<span class="br0">)</span></span></span> &#23454;&#29616;&#36816;&#31639;&#19968;&#33324;&#22788;&#29702;&#38169;&#35823;&#21644;&#29305;&#27530;&#24773;&#20917;&#12290;</p>
<h3><span class="mw-headline" id=".E6.B3.A8.E6.84.8F">&#27880;&#24847;</span></h3>
<p>&#21453;&#27491;&#20999;&#65288;&#25110;&#24359;&#27491;&#20999;&#65289;&#26159;&#22810;&#20540;&#20989;&#25968;&#32780;&#35201;&#27714;&#22797;&#24179;&#38754;&#19978;&#30340;&#20998;&#25903;&#20999;&#21106;&#12290;&#32422;&#23450;&#20998;&#25903;&#20999;&#21106;&#32622;&#20110;&#34394;&#36724;&#30340;&#32447;&#27573; <span class="texhtml" style="white-space: nowrap;">(-&infin;i,-i)</span> &#21644; <span class="texhtml" style="white-space: nowrap;">(+i,+&infin;i)</span> &#19978;&#12290;</p>
&#21453;&#27491;&#20999;&#20027;&#20540;&#30340;&#25968;&#23398;&#23450;&#20041;&#26159; <span class="texhtml" style="white-space: nowrap;">atan z = -<span class="t-mfrac"></span></span>
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<td>1</td>
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<td>2</td>
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i [ln(1 - iz) - ln (1 + iz] &#12290;
<h3><span class="mw-headline" id=".E7.A4.BA.E4.BE.8B">&#31034;&#20363;</span></h3>
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<pre class="de1"><span class="co2">#include &lt;stdio.h&gt;</span>
<span class="co2">#include &lt;float.h&gt;</span>
<span class="co2">#include &lt;complex.h&gt;</span>
<span class="kw4">int</span> main<span class="br0">(</span><span class="kw4">void</span><span class="br0">)</span>
<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="sy1">=</span> catan<span class="br0">(</span><span class="nu0">2</span><span class="sy2">*</span>I<span class="br0">)</span><span class="sy4">;</span>
<a href="c-io-fprintf.html"><span class="kw848">printf</span></a><span class="br0">(</span><span class="st0">&quot;catan(+0+2i) = %f%+fi<span class="es1">\n</span>&quot;</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>
<span class="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a> z2 <span class="sy1">=</span> catan<span class="br0">(</span><span class="sy2">-</span><a href="c-numeric-complex-conj.html"><span class="kw760">conj</span></a><span class="br0">(</span><span class="nu0">2</span><span class="sy2">*</span>I<span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// &#25110; CMPLX(-0.0, 2)</span>
<a href="c-io-fprintf.html"><span class="kw848">printf</span></a><span class="br0">(</span><span class="st0">&quot;catan(-0+2i) (the other side of the cut) = %f%+fi<span class="es1">\n</span>&quot;</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>
<span class="kw4">double</span> <a href="c-numeric-complex-complex.html"><span class="kw743">complex</span></a> z3 <span class="sy1">=</span> <span class="nu0">2</span><span class="sy2">*</span>catan<span class="br0">(</span><span class="nu0">2</span><span class="sy2">*</span>I<span class="sy2">*</span><a href="c-types-limits.html"><span class="kw378">DBL_MAX</span></a><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// &#25110; CMPLX(0, INFINITY)</span>
<a href="c-io-fprintf.html"><span class="kw848">printf</span></a><span class="br0">(</span><span class="st0">&quot;2*catan(+0+i*Inf) = %f%+fi<span class="es1">\n</span>&quot;</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>
<span class="br0">}</span></pre></div>
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<p>&#36755;&#20986;&#65306;</p>
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<pre class="de1">catan(+0+2i) = 1.570796+0.549306i
catan(-0+2i) (the other side of the cut) = -1.570796+0.549306i
2*catan(+0+i*Inf) = 3.141593+0.000000i</pre></div>
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<h3><span class="mw-headline" id=".E5.BC.95.E7.94.A8">&#24341;&#29992;</span></h3>
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<li>C11 &#26631;&#20934;&#65288;ISO/IEC 9899:2011&#65289;&#65306;</li>
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<li>7.3.5.3 The catan functions (p: 191)</li>
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<li>7.25 Type-generic math &lt;tgmath.h&gt; (p: 373-375)</li>
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<li>G.7 Type-generic math &lt;tgmath.h&gt; (p: 545)</li>
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<li>C99 &#26631;&#20934;&#65288;ISO/IEC 9899:1999&#65289;&#65306;</li>
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<li>7.3.5.3 The catan functions (p: 173)</li>
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<li>7.22 Type-generic math &lt;tgmath.h&gt; (p: 335-337)</li>
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</dd>
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<li>G.7 Type-generic math &lt;tgmath.h&gt; (p: 480)</li>
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<h3><span class="mw-headline" id=".E5.8F.82.E9.98.85">&#21442;&#38405;</span></h3>
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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>
<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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<td>&#35745;&#31639;&#22797;&#25968;&#21453;&#27491;&#24358;<br />
<span class="t-mark">(&#20989;&#25968;)</span></td>
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<div><a href="c-numeric-complex-cacos.html"><span class="t-lines"><span>cacos</span><span>cacosf</span><span>cacosl</span></span></a></div>
<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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<td>&#35745;&#31639;&#22797;&#25968;&#21453;&#20313;&#24358;<br />
<span class="t-mark">(&#20989;&#25968;)</span></td>
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<div><a href="c-numeric-complex-ctan.html"><span class="t-lines"><span>ctan</span><span>ctanf</span><span>ctanl</span></span></a></div>
<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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<td>&#35745;&#31639;&#22797;&#25968;&#27491;&#20999;<br />
<span class="t-mark">(&#20989;&#25968;)</span></td>
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<div><a href="c-numeric-math-atan.html"><span class="t-lines"><span>atan</span><span>atanf</span><span>atanl</span></span></a></div>
<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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<td>&#35745;&#31639;&#21453;&#27491;&#20999;&#65288; <span class="mjax" style="display:none">\({\small\arctan{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arctan(x)</span> &#65289;<br />
<span class="t-mark">(&#20989;&#25968;)</span></td>
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