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<div class="header">
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<p>
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Next: <a href="hypot.html#hypot" accesskey="n" rel="next">hypot</a>, Previous: <a href="frexp.html#frexp" accesskey="p" rel="prev">frexp</a>, Up: <a href="Math.html#Math" accesskey="u" rel="up">Math</a> [<a href="Document-Index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Document-Index.html#Document-Index" title="Index" rel="index">Index</a>]</p>
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<a name="gamma_002c-gammaf_002c-lgamma_002c-lgammaf_002c-gamma_005fr_002c-gammaf_005fr_002c-lgamma_005fr_002c-lgammaf_005fr_002c-tgamma_002c-and-tgammaf_002d_002d_002dlogarithmic-and-plain-gamma-functions"></a>
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<h3 class="section">1.27 <code>gamma</code>, <code>gammaf</code>, <code>lgamma</code>, <code>lgammaf</code>, <code>gamma_r</code>, <code>gammaf_r</code>, <code>lgamma_r</code>, <code>lgammaf_r</code>, <code>tgamma</code>, and <code>tgammaf</code>—logarithmic and plain gamma functions</h3>
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<a name="index-gamma"></a>
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<a name="index-gammaf"></a>
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<a name="index-lgamma"></a>
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<a name="index-lgammaf"></a>
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<a name="index-gamma_005fr"></a>
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<a name="index-gammaf_005fr"></a>
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<a name="index-lgamma_005fr"></a>
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<a name="index-lgammaf_005fr"></a>
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<a name="index-tgamma"></a>
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<a name="index-tgammaf"></a>
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<p><strong>Synopsis</strong>
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</p><div class="example">
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<pre class="example">#include <math.h>
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double gamma(double <var>x</var>);
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float gammaf(float <var>x</var>);
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double lgamma(double <var>x</var>);
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float lgammaf(float <var>x</var>);
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double gamma_r(double <var>x</var>, int *<var>signgamp</var>);
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float gammaf_r(float <var>x</var>, int *<var>signgamp</var>);
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double lgamma_r(double <var>x</var>, int *<var>signgamp</var>);
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float lgammaf_r(float <var>x</var>, int *<var>signgamp</var>);
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double tgamma(double <var>x</var>);
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float tgammaf(float <var>x</var>);
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</pre></div>
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<p><strong>Description</strong><br>
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<code>gamma</code> calculates
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the natural logarithm of the gamma function of <var>x</var>. The gamma function
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(<code>exp(gamma(<var>x</var>))</code>) is a generalization of factorial, and retains
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the property that
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<code>exp(gamma(N))</code> is equivalent to <code>N*exp(gamma(N-1))</code>.
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Accordingly, the results of the gamma function itself grow very
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quickly. <code>gamma</code> is defined as
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the natural log of the gamma function, rather than the gamma function
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itself,
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to extend the useful range of results representable.
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</p>
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<p>The sign of the result is returned in the global variable <code>signgam</code>,
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which is declared in math.h.
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</p>
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<p><code>gammaf</code> performs the same calculation as <code>gamma</code>, but uses and
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returns <code>float</code> values.
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</p>
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<p><code>lgamma</code> and <code>lgammaf</code> are alternate names for <code>gamma</code> and
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<code>gammaf</code>. The use of <code>lgamma</code> instead of <code>gamma</code> is a reminder
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that these functions compute the log of the gamma function, rather
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than the gamma function itself.
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</p>
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<p>The functions <code>gamma_r</code>, <code>gammaf_r</code>, <code>lgamma_r</code>, and
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<code>lgammaf_r</code> are just like <code>gamma</code>, <code>gammaf</code>, <code>lgamma</code>, and
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<code>lgammaf</code>, respectively, but take an additional argument. This
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additional argument is a pointer to an integer. This additional
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argument is used to return the sign of the result, and the global
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variable <code>signgam</code> is not used. These functions may be used for
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reentrant calls (but they will still set the global variable <code>errno</code>
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if an error occurs).
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</p>
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<p><code>tgamma</code> and <code>tgammaf</code> are the "true gamma" functions, returning
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the gamma function of <var>x</var>–without a logarithm.
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(They are apparently so named because of the prior existence of the old,
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poorly-named <code>gamma</code> functions which returned the log of gamma up
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through BSD 4.2.)
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</p>
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<br>
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<p><strong>Returns</strong><br>
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Normally, the computed result is returned.
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</p>
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<p>When <var>x</var> is a nonpositive integer, <code>gamma</code> returns <code>HUGE_VAL</code>
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and <code>errno</code> is set to <code>EDOM</code>. If the result overflows, <code>gamma</code>
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returns <code>HUGE_VAL</code> and <code>errno</code> is set to <code>ERANGE</code>.
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</p>
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<br>
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<p><strong>Portability</strong><br>
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Neither <code>gamma</code> nor <code>gammaf</code> is ANSI C. It is better not to use either
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of these; use <code>lgamma</code> or <code>tgamma</code> instead.<br>
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<code>lgamma</code>, <code>lgammaf</code>, <code>tgamma</code>, and <code>tgammaf</code> are nominally C standard
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in terms of the base return values, although the <var>signgam</var> global for
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<code>lgamma</code> is not standard.
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</p>
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<br>
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<hr>
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<div class="header">
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<p>
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Next: <a href="hypot.html#hypot" accesskey="n" rel="next">hypot</a>, Previous: <a href="frexp.html#frexp" accesskey="p" rel="prev">frexp</a>, Up: <a href="Math.html#Math" accesskey="u" rel="up">Math</a> [<a href="Document-Index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Document-Index.html#Document-Index" title="Index" rel="index">Index</a>]</p>
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