211 lines
16 KiB
HTML
211 lines
16 KiB
HTML
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<title>tgamma, tgammaf, tgammal</title>
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<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-c_numeric_math_tgamma skin-cppreference2 action-view cpp-navbar">
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<h1 id="firstHeading" class="firstHeading">tgamma, tgammaf, tgammal</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-math.html">math</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><math.h></code></div>
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</td>
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<td></td>
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<div><span class="mw-geshi c source-c"><span class="kw4">float</span> tgammaf<span class="br0">(</span> <span class="kw4">float</span> arg <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> tgamma<span class="br0">(</span> <span class="kw4">double</span> arg <span class="br0">)</span><span class="sy4">;</span></span></div>
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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> tgammal<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> arg <span class="br0">)</span><span class="sy4">;</span></span></div>
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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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<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 tgamma( arg )</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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<div class="t-li1"><span class="t-li">1-3)</span> 计算 <code>arg</code> 的<a href="https://en.wikipedia.org/wiki/Gamma_function" class="extiw" title="enwiki:Gamma function">伽马函数</a>。</div>
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<div class="t-li1"><span class="t-li">4)</span> 泛型宏：若 <code>arg</code> 拥有 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span></span></span> 类型，则调用 <code>tgammal</code> 。否则，若 <code>arg</code> 拥有整数类型或 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">double</span></span></span> 类型，则调用 <code>tgamma</code> 。否则调用 <code>tgammaf</code> 。</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>arg</td>
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<td>-</td>
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<td>浮点值</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>arg</code> 的 Γ 函数值，即 <span class="mjax" style="display:none">\(\Gamma(\mathtt{arg}) = \displaystyle\int_0^\infty\!\! t^{\mathtt{arg}-1} e^{-t}\, dt\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;"><span style="font-size: 1.3em; vertical-align:-0.08em; margin-right: 0.08em;">∫</span><span class="t-su t-su-b">∞<br />
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0</span><i>t</i><span class="t-su">arg-1<br /></span> <i>e</i><sup>-t</sup> d<i>t</i></span> 。</p>
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<p>若出现定义域错误，则返回实现定义值（受支持平台上为 NaN ）。</p>
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<p>若出现极点错误，则返回 <code>±HUGE_VAL</code> 、 <code>±HUGE_VALF</code> 或 <code>±HUGE_VALL</code> 。</p>
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<p>若出现上溢所致的值域错误，则返回 <code>±HUGE_VAL</code> 、 <code>±HUGE_VALF</code> 或 <code>±HUGE_VALL</code> 。</p>
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<p>若出现下溢所致的值域错误，则返回（舍入后的）正确结果。</p>
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<h3><span class="mw-headline" id=".E9.94.99.E8.AF.AF.E5.A4.84.E7.90.86">错误处理</span></h3>
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<p>报告 <a href="c-numeric-math-math_errhandling.html"><tt>math_errhandling</tt></a> 中指定的错误</p>
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<p>若 <code>arg</code> 为零或为小于零的整数，则可能出现极点或定义域错误。</p>
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<p>若实现支持 IEEE 浮点算术（ IEC 60559 ），则</p>
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<ul>
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<li>若参数为 ±0 ，则返回 ±∞ 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>若参数为负整数，则返回 NaN 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>若参数为 -∞ ，则返回 NaN 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>若参数为 +∞ ，则返回 +∞</li>
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<li>若参数为 NaN ，则返回 NaN</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>若 <code>arg</code> 为自然数，则 <span class="t-c"><span class="mw-geshi c source-c">tgamma<span class="br0">(</span>arg<span class="br0">)</span></span></span> 为 <code>arg-1</code> 的阶乘。许多实现若参数是足够小的整数，则计算准确的整数域阶乘。</p>
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<p>对于 IEEE 兼容的 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">double</span></span></span> 类型，若 <code>0 < x < 1/DBL_MAX</code> 或 <code>x > 171.7</code> 则发生上溢。</p>
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<p><a rel="nofollow" class="external text" href="http://pubs.opengroup.org/onlinepubs/9699919799/functions/tgamma.html">POSIX 要求</a>若参数为零则出现极点错误，但在参数为负整数时出现定义域错误。它亦指定在将来，对于负整数，定义域错误可能被替换成浮点错误（这些情况下返回值将从 NaN 更改为 ±∞ ）。</p>
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<p>多数实现中有名为 <code>gamma</code> 的非标准函数，但其定义不一致。例如， <code>gamma</code> 的 glibc 和 4.2BSD 版本执行 <code>lgamma</code> ，但 <code>gamma</code> 的 4.4BSD 版本执行 <code>tgamma</code> 。</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 <float.h></span>
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<span class="co2">#include <errno.h></span>
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<span class="co2">#include <fenv.h></span>
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<span class="co2">#pragma STDC FENV_ACCESS ON</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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<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"tgamma(10) = %f, 9!=%f<span class="es1">\n</span>"</span>, tgamma<span class="br0">(</span><span class="nu0">10</span><span class="br0">)</span>, <span class="nu0">2</span><span class="sy2">*</span><span class="nu0">3</span><span class="sy2">*</span><span class="nu0">4</span><span class="sy2">*</span><span class="nu0">5</span><span class="sy2">*</span><span class="nu0">6</span><span class="sy2">*</span><span class="nu0">7</span><span class="sy2">*</span><span class="nu0">8</span><span class="sy2">*</span><span class="nu16">9.0</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"tgamma(0.5) = %f, sqrt(pi) = %f<span class="es1">\n</span>"</span>, <a href="c-numeric-math-sqrt.html"><span class="kw665">sqrt</span></a><span class="br0">(</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="br0">)</span>, tgamma<span class="br0">(</span><span class="nu16">0.5</span><span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="co1">// 特殊值</span>
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<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"tgamma(+Inf) = %f<span class="es1">\n</span>"</span>, tgamma<span class="br0">(</span>INFINITY<span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="co1">// 错误处理</span>
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<span class="kw2">errno</span> <span class="sy1">=</span> <span class="nu0">0</span><span class="sy4">;</span> <a href="c-numeric-fenv-feclearexcept.html"><span class="kw717">feclearexcept</span></a><span class="br0">(</span><a href="c-numeric-fenv-FE_exceptions.html"><span class="kw728">FE_ALL_EXCEPT</span></a><span class="br0">)</span><span class="sy4">;</span>
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<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"tgamma(-1) = %f<span class="es1">\n</span>"</span>, tgamma<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>
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<span class="kw1">if</span><span class="br0">(</span><span class="kw2">errno</span> <span class="sy1">==</span> <a href="c-error-errno_macros.html"><span class="kw478">ERANGE</span></a><span class="br0">)</span> <a href="c-io-perror.html"><span class="kw878">perror</span></a><span class="br0">(</span><span class="st0">" errno == ERANGE"</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="kw1">else</span> <span class="kw1">if</span><span class="br0">(</span><span class="kw2">errno</span> <span class="sy1">==</span> <a href="c-error-errno_macros.html"><span class="kw426">EDOM</span></a><span class="br0">)</span> <a href="c-io-perror.html"><span class="kw878">perror</span></a><span class="br0">(</span><span class="st0">" errno == EDOM"</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="kw1">if</span><span class="br0">(</span><a href="c-numeric-fenv-fetestexcept.html"><span class="kw718">fetestexcept</span></a><span class="br0">(</span><a href="c-numeric-fenv-FE_exceptions.html"><span class="kw729">FE_DIVBYZERO</span></a><span class="br0">)</span><span class="br0">)</span> <a href="c-io-puts.html"><span class="kw835">puts</span></a><span class="br0">(</span><span class="st0">" FE_DIVBYZERO raised"</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="kw1">else</span> <span class="kw1">if</span><span class="br0">(</span><a href="c-numeric-fenv-fetestexcept.html"><span class="kw718">fetestexcept</span></a><span class="br0">(</span><a href="c-numeric-fenv-FE_exceptions.html"><span class="kw731">FE_INVALID</span></a><span class="br0">)</span><span class="br0">)</span> <a href="c-io-puts.html"><span class="kw835">puts</span></a><span class="br0">(</span><span class="st0">" FE_INVALID raised"</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>可能的输出：</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">tgamma(10) = 362880.000000, 9!=362880.000000
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tgamma(0.5) = 1.772454, sqrt(pi) = 1.772454
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tgamma(+Inf) = inf
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tgamma(-1) = nan
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errno == EDOM: Numerical argument out of domain
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FE_INVALID raised</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>7.12.8.4 The tgamma functions (p: 250)</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>F.10.5.4 The tgamma functions (p: 525)</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>7.12.8.4 The tgamma functions (p: 231)</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>F.9.5.4 The tgamma functions (p: 462)</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-math-lgamma.html"><span class="t-lines"><span>lgamma</span><span>lgammaf</span><span>lgammal</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>计算伽马函数的自然对数（底为 <i>e</i> ）<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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<h3><span class="mw-headline" id=".E5.A4.96.E9.83.A8.E9.93.BE.E6.8E.A5">外部链接</span></h3>
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<a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/GammaFunction.html">Weisstein, Eric W. “伽马函数”</a>来自 MathWorld--A Wolfram Web Resource 。</div>
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</div>
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<div class="visualClear"></div>
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