351 lines
6.1 KiB
HTML
351 lines
6.1 KiB
HTML
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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<HTML><HEAD><TITLE>Man page of TGAMMA</TITLE>
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</HEAD><BODY>
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<H1>TGAMMA</H1>
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Section: Linux Programmer's Manual (3)<BR>Updated: 2017-09-15<BR><A HREF="#index">Index</A>
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<A HREF="/cgi-bin/man/man2html">Return to Main Contents</A><HR>
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<A NAME="lbAB"> </A>
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<H2>NAME</H2>
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tgamma, tgammaf, tgammal - true gamma function
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<A NAME="lbAC"> </A>
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<H2>SYNOPSIS</H2>
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<B>#include <<A HREF="file:///usr/include/math.h">math.h</A>></B>
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<P>
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<B>double tgamma(double </B><I>x</I><B>);</B>
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<BR>
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<B>float tgammaf(float </B><I>x</I><B>);</B>
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<BR>
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<B>long double tgammal(long double </B><I>x</I><B>);</B>
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<P>
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Link with <I>-lm</I>.
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<P>
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Feature Test Macro Requirements for glibc (see
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<B><A HREF="/cgi-bin/man/man2html?7+feature_test_macros">feature_test_macros</A></B>(7)):
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<P>
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<B>tgamma</B>(),
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<B>tgammaf</B>(),
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<B>tgammal</B>():
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<DL COMPACT><DT id="1"><DD>
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_ISOC99_SOURCE ||
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_POSIX_C_SOURCE >= 200112L
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</DL>
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<A NAME="lbAD"> </A>
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<H2>DESCRIPTION</H2>
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These functions calculate the Gamma function of
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<I>x</I>.
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<P>
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The Gamma function is defined by
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<P>
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<DL COMPACT><DT id="2"><DD>
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Gamma(x) = integral from 0 to infinity of t^(x-1) e^-t dt
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</DL>
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<P>
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It is defined for every real number except for nonpositive integers.
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For nonnegative integral
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<I>m</I>
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one has
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<P>
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<DL COMPACT><DT id="3"><DD>
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Gamma(m+1) = m!
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</DL>
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<P>
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and, more generally, for all
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<I>x</I>:
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<P>
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<DL COMPACT><DT id="4"><DD>
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Gamma(x+1) = x * Gamma(x)
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</DL>
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<P>
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Furthermore, the following is valid for all values of
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<I>x</I>
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outside the poles:
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<P>
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<DL COMPACT><DT id="5"><DD>
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Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)
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</DL>
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<A NAME="lbAE"> </A>
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<H2>RETURN VALUE</H2>
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On success, these functions return Gamma(x).
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<P>
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If
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<I>x</I>
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is a NaN, a NaN is returned.
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<P>
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If
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<I>x</I>
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is positive infinity, positive infinity is returned.
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<P>
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If
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<I>x</I>
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is a negative integer, or is negative infinity,
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a domain error occurs,
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and a NaN is returned.
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<P>
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If the result overflows,
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a range error occurs,
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and the functions return
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<B>HUGE_VAL</B>,
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<B>HUGE_VALF</B>,
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or
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<B>HUGE_VALL</B>,
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respectively, with the correct mathematical sign.
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<P>
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If the result underflows,
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a range error occurs,
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and the functions return 0, with the correct mathematical sign.
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<P>
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If
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<I>x</I>
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is -0 or +0,
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a pole error occurs,
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and the functions return
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<B>HUGE_VAL</B>,
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<B>HUGE_VALF</B>,
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or
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<B>HUGE_VALL</B>,
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respectively, with the same sign as the 0.
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<A NAME="lbAF"> </A>
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<H2>ERRORS</H2>
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See
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<B><A HREF="/cgi-bin/man/man2html?7+math_error">math_error</A></B>(7)
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for information on how to determine whether an error has occurred
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when calling these functions.
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<P>
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The following errors can occur:
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<DL COMPACT>
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<DT id="6">Domain error: <I>x</I> is a negative integer, or negative infinity<DD>
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<I>errno</I>
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is set to
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<B>EDOM</B>.
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An invalid floating-point exception
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(<B>FE_INVALID</B>)
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is raised (but see BUGS).
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<DT id="7">Pole error: <I>x</I> is +0 or -0<DD>
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<I>errno</I>
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is set to
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<B>ERANGE</B>.
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A divide-by-zero floating-point exception
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(<B>FE_DIVBYZERO</B>)
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is raised.
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<DT id="8">Range error: result overflow<DD>
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<I>errno</I>
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is set to
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<B>ERANGE</B>.
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An overflow floating-point exception
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(<B>FE_OVERFLOW</B>)
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is raised.
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</DL>
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<P>
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glibc also gives the following error which is not specified
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in C99 or POSIX.1-2001.
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<DL COMPACT>
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<DT id="9">Range error: result underflow<DD>
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An underflow floating-point exception
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(<B>FE_UNDERFLOW</B>)
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is raised, and
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<I>errno</I>
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is set to
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<B>ERANGE</B>.
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</DL>
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<A NAME="lbAG"> </A>
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<H2>VERSIONS</H2>
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These functions first appeared in glibc in version 2.1.
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<A NAME="lbAH"> </A>
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<H2>ATTRIBUTES</H2>
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For an explanation of the terms used in this section, see
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<B><A HREF="/cgi-bin/man/man2html?7+attributes">attributes</A></B>(7).
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<TABLE BORDER>
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<TR VALIGN=top><TD><B>Interface</B></TD><TD><B>Attribute</B></TD><TD><B>Value</B><BR></TD></TR>
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<TR VALIGN=top><TD>
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<B>tgamma</B>(),
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<B>tgammaf</B>(),
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<B>tgammal</B>()
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</TD><TD>Thread safety</TD><TD>MT-Safe<BR></TD></TR>
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</TABLE>
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<A NAME="lbAI"> </A>
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<H2>CONFORMING TO</H2>
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C99, POSIX.1-2001, POSIX.1-2008.
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<A NAME="lbAJ"> </A>
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<H2>NOTES</H2>
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This function had to be called "true gamma function"
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since there is already a function
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<B><A HREF="/cgi-bin/man/man2html?3+gamma">gamma</A></B>(3)
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that returns something else (see
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<B><A HREF="/cgi-bin/man/man2html?3+gamma">gamma</A></B>(3)
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for details).
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<A NAME="lbAK"> </A>
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<H2>BUGS</H2>
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Before version 2.18, the glibc implementation of these functions did not set
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<I>errno</I>
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to
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<B>EDOM</B>
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when
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<I>x</I>
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is negative infinity.
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<P>
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Before glibc 2.19,
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the glibc implementation of these functions did not set
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<I>errno</I>
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to
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<B>ERANGE</B>
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on an underflow range error.
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<I>x</I>
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<P>
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In glibc versions 2.3.3 and earlier,
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an argument of +0 or -0 incorrectly produced a domain error
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(<I>errno</I>
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set to
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<B>EDOM</B>
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and an
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<B>FE_INVALID</B>
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exception raised), rather than a pole error.
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<A NAME="lbAL"> </A>
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<H2>SEE ALSO</H2>
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<B><A HREF="/cgi-bin/man/man2html?3+gamma">gamma</A></B>(3),
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<B><A HREF="/cgi-bin/man/man2html?3+lgamma">lgamma</A></B>(3)
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<A NAME="lbAM"> </A>
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<H2>COLOPHON</H2>
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This page is part of release 5.05 of the Linux
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<I>man-pages</I>
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project.
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A description of the project,
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information about reporting bugs,
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and the latest version of this page,
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can be found at
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<A HREF="https://www.kernel.org/doc/man-pages/.">https://www.kernel.org/doc/man-pages/.</A>
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<P>
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<HR>
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<A NAME="index"> </A><H2>Index</H2>
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<DL>
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<DT id="10"><A HREF="#lbAB">NAME</A><DD>
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<DT id="11"><A HREF="#lbAC">SYNOPSIS</A><DD>
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<DT id="12"><A HREF="#lbAD">DESCRIPTION</A><DD>
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<DT id="13"><A HREF="#lbAE">RETURN VALUE</A><DD>
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<DT id="14"><A HREF="#lbAF">ERRORS</A><DD>
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<DT id="15"><A HREF="#lbAG">VERSIONS</A><DD>
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<DT id="16"><A HREF="#lbAH">ATTRIBUTES</A><DD>
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<DT id="17"><A HREF="#lbAI">CONFORMING TO</A><DD>
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<DT id="18"><A HREF="#lbAJ">NOTES</A><DD>
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<DT id="19"><A HREF="#lbAK">BUGS</A><DD>
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<DT id="20"><A HREF="#lbAL">SEE ALSO</A><DD>
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<DT id="21"><A HREF="#lbAM">COLOPHON</A><DD>
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</DL>
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<HR>
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This document was created by
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<A HREF="/cgi-bin/man/man2html">man2html</A>,
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using the manual pages.<BR>
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Time: 00:05:58 GMT, March 31, 2021
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</BODY>
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