169 lines
17 KiB
HTML
169 lines
17 KiB
HTML
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<title>std::tgamma, std::tgammaf, std::tgammal</title>
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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>tgamma, <span style="font-size:0.7em; line-height:130%">std::</span>tgammaf, <span style="font-size:0.7em; line-height:130%">std::</span>tgammal</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-math.html">math</a></span></div>
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<div>定义于头文件 <code><a href="cpp-header-cmath.html"><cmath></a></code></div>
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<td></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">float</span> tgamma <span class="br0">(</span> <span class="kw4">float</span> arg <span class="br0">)</span><span class="sy4">;</span><br />
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<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>(1)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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<div><span class="mw-geshi cpp source-cpp"><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-cxx11">(C++11 起)</span></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span> tgamma <span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> arg <span class="br0">)</span><span class="sy4">;</span><br />
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<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-cxx11">(C++11 起)</span></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span> tgamma <span class="br0">(</span> IntegralType arg <span class="br0">)</span><span class="sy4">;</span></span></div>
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<td>(4)</td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 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">gamma 函数</a>。</div>
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<div class="t-li1"><span class="t-li">4)</span> 接受任何<a href="cpp-types-is_integral.html">整数类型</a>参数的重载集或函数模板。等价于 2) （将参数转型为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> ）。</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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<td>arg</td>
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<td>-</td>
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<td>浮点或<a href="cpp-types-is_integral.html">整数类型</a>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 <span class="t-lc"><a href="cpp-numeric-math-math_errhandling.html">math_errhandling</a></span> 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="cpp-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="cpp-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="cpp-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 cpp source-cpp">std<span class="sy4">::</span><span class="me2">tgamma</span><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 cpp source-cpp"><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，可能替换定义域错误为浮点错误（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="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 <cerrno></span>
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<span class="co2">#include <cstring></span>
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<span class="co2">#include <cfenv></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="br0">)</span>
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<span class="br0">{</span>
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<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"tgamma(10) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">tgamma</span><span class="br0">(</span><span class="nu0">10</span><span class="br0">)</span>
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<span class="sy1"><<</span> <span class="st0">", 9! = "</span> <span class="sy1"><<</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="nu0">9</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span>
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<span class="sy1"><<</span> <span class="st0">"tgamma(0.5) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">tgamma</span><span class="br0">(</span><span class="nu16">0.5</span><span class="br0">)</span>
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<span class="sy1"><<</span> <span class="st0">", sqrt(pi) = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-math-sqrt.html"><span class="kw1329">std::<span class="me2">sqrt</span></span></a><span class="br0">(</span><a href="cpp-numeric-math-acos.html"><span class="kw1337">std::<span class="me2">acos</span></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="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
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<span class="co1">// 特殊值</span>
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<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"tgamma(1) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">tgamma</span><span class="br0">(</span><span class="nu0">1</span><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span>
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<span class="sy1"><<</span> <span class="st0">"tgamma(+Inf) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">tgamma</span><span class="br0">(</span><a href="cpp-numeric-math-INFINITY.html"><span class="kw1376">INFINITY</span></a><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="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>
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<a href="cpp-numeric-fenv-feclearexcept.html"><span class="kw1449">std::<span class="me2">feclearexcept</span></span></a><span class="br0">(</span><a href="cpp-numeric-fenv-FE_exceptions.html"><span class="kw1460">FE_ALL_EXCEPT</span></a><span class="br0">)</span><span class="sy4">;</span>
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<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"tgamma(-1) = "</span> <span class="sy1"><<</span> std<span class="sy4">::</span><span class="me2">tgamma</span><span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span><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="kw1">if</span> <span class="br0">(</span><span class="kw2">errno</span> <span class="sy1">==</span> <a href="cpp-error-errno_macros.html"><span class="kw810">EDOM</span></a><span class="br0">)</span>
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<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">" errno == EDOM: "</span> <span class="sy1"><<</span> <a href="cpp-string-byte-strerror.html"><span class="kw1161">std::<span class="me2">strerror</span></span></a><span class="br0">(</span><span class="kw2">errno</span><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="kw1">if</span> <span class="br0">(</span><a href="cpp-numeric-fenv-fetestexcept.html"><span class="kw1450">std::<span class="me2">fetestexcept</span></span></a><span class="br0">(</span><a href="cpp-numeric-fenv-FE_exceptions.html"><span class="kw1463">FE_INVALID</span></a><span class="br0">)</span><span class="br0">)</span>
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<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">" FE_INVALID raised<span class="es1">\n</span>"</span><span class="sy4">;</span>
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<span class="br0">}</span></pre></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, 9! = 362880
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tgamma(0.5) = 1.77245, sqrt(pi) = 1.77245
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tgamma(1) = 1
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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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<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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<div class="t-dsc-member-div">
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<div><a href="cpp-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-cxx11">(C++11)</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>
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<td>gamma 函数的自然对数<br />
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<span class="t-mark">(函数)</span></td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-special_functions-beta.html"><span class="t-lines"><span>beta</span><span>betaf</span><span>betal</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span></span></div>
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</div>
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</td>
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<td>beta 函数<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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<p><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 。</p>
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</div>
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<div class="visualClear"></div>
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