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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>&mdash;logarithmic and plain gamma functions</h3>
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<p><strong>Synopsis</strong>
</p><div class="example">
<pre class="example">#include &lt;math.h&gt;
double gamma(double <var>x</var>);
float gammaf(float <var>x</var>);
double lgamma(double <var>x</var>);
float lgammaf(float <var>x</var>);
double gamma_r(double <var>x</var>, int *<var>signgamp</var>);
float gammaf_r(float <var>x</var>, int *<var>signgamp</var>);
double lgamma_r(double <var>x</var>, int *<var>signgamp</var>);
float lgammaf_r(float <var>x</var>, int *<var>signgamp</var>);
double tgamma(double <var>x</var>);
float tgammaf(float <var>x</var>);

</pre></div>
<p><strong>Description</strong><br>
<code>gamma</code> calculates
the natural logarithm of the gamma function of <var>x</var>.  The gamma function
(<code>exp(gamma(<var>x</var>))</code>) is a generalization of factorial, and retains
the property that
<code>exp(gamma(N))</code> is equivalent to <code>N*exp(gamma(N-1))</code>.
Accordingly, the results of the gamma function itself grow very
quickly.  <code>gamma</code> is defined as
the natural log of the gamma function, rather than the gamma function
itself,
to extend the useful range of results representable.
</p>
<p>The sign of the result is returned in the global variable <code>signgam</code>,
which is declared in math.h.
</p>
<p><code>gammaf</code> performs the same calculation as <code>gamma</code>, but uses and
returns <code>float</code> values.
</p>
<p><code>lgamma</code> and <code>lgammaf</code> are alternate names for <code>gamma</code> and
<code>gammaf</code>.  The use of <code>lgamma</code> instead of <code>gamma</code> is a reminder
that these functions compute the log of the gamma function, rather
than the gamma function itself.
</p>
<p>The functions <code>gamma_r</code>, <code>gammaf_r</code>, <code>lgamma_r</code>, and
<code>lgammaf_r</code> are just like <code>gamma</code>, <code>gammaf</code>, <code>lgamma</code>, and
<code>lgammaf</code>, respectively, but take an additional argument.  This
additional argument is a pointer to an integer.  This additional
argument is used to return the sign of the result, and the global
variable <code>signgam</code> is not used.  These functions may be used for
reentrant calls (but they will still set the global variable <code>errno</code>
if an error occurs).
</p>
<p><code>tgamma</code> and <code>tgammaf</code> are the &quot;true gamma&quot; functions, returning
the gamma function of <var>x</var>&ndash;without a logarithm.
(They are apparently so named because of the prior existence of the old,
poorly-named <code>gamma</code> functions which returned the log of gamma up
through BSD 4.2.)
</p>
<br>
<p><strong>Returns</strong><br>
Normally, the computed result is returned.
</p>
<p>When <var>x</var> is a nonpositive integer, <code>gamma</code> returns <code>HUGE_VAL</code>
and <code>errno</code> is set to <code>EDOM</code>.  If the result overflows, <code>gamma</code>
returns <code>HUGE_VAL</code> and <code>errno</code> is set to <code>ERANGE</code>.
</p>
<br>
<p><strong>Portability</strong><br>
Neither <code>gamma</code> nor <code>gammaf</code> is ANSI C.  It is better not to use either
of these; use <code>lgamma</code> or <code>tgamma</code> instead.<br>
<code>lgamma</code>, <code>lgammaf</code>, <code>tgamma</code>, and <code>tgammaf</code> are nominally C standard
in terms of the base return values, although the <var>signgam</var> global for
<code>lgamma</code> is not standard.
</p>
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