mirror of https://github.com/mkerrisk/man-pages
166 lines
3.6 KiB
Groff
166 lines
3.6 KiB
Groff
.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
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.\" Distributed under GPL
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.\" Based on glibc infopages
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.\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk
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.\" <mtk.manpages@gmail.com>
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.\" Modified 2004-11-15, fixed error noted by Fabian Kreutz
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.\" <kreutz@dbs.uni-hannover.de>
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.TH TGAMMA 3 2008-08-05 "GNU" "Linux Programmer's Manual"
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.SH NAME
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tgamma, tgammaf, tgammal \- true gamma function
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.SH SYNOPSIS
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.B #include <math.h>
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.sp
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.BI "double tgamma(double " x );
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.br
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.BI "float tgammaf(float " x );
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.br
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.BI "long double tgammal(long double " x );
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.sp
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Link with \fI\-lm\fP.
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.sp
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.in -4n
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Feature Test Macro Requirements for glibc (see
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.BR feature_test_macros (7)):
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.in
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.sp
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.ad l
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.BR tgamma (),
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.BR tgammaf (),
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.BR tgammal ():
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_XOPEN_SOURCE\ >=\ 600 || _ISOC99_SOURCE; or
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.I cc\ -std=c99
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.ad b
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.SH DESCRIPTION
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The Gamma function is defined by
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.sp
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Gamma(x) = integral from 0 to infinity of t^(x\-1) e^\-t dt
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.sp
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It is defined for every real number except for non-positive integers.
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For non-negative integral \fIm\fP one has
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.sp
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Gamma(m+1) = m!
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.sp
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and, more generally, for all \fIx\fP:
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.sp
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Gamma(x+1) = x * Gamma(x)
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.sp
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Furthermore, the following is valid for all values of \fIx\fP
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outside the poles:
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.sp
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Gamma(x) * Gamma(1 \- x) = PI / sin(PI * x)
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.PP
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.SH RETURN VALUE
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On success, these functions return Gamma(x).
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If
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.I x
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is a NaN, a NaN is returned.
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If
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.I x
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is positive infinity, positive infinity is returned.
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If
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.I x
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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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If the result overflows,
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a "range error" occurs,
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and the functions return
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.BR HUGE_VAL ,
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.BR HUGE_VALF ,
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or
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.BR HUGE_VALL ,
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respectively, with the correct mathematical sign.
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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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If
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.I x
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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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.BR HUGE_VAL ,
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.BR HUGE_VALF ,
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or
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.BR HUGE_VALL ,
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respectively, with the same sign as the 0.
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.SH ERRORS
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See
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.BR math_error (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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.PP
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The following errors can occur:
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.TP
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Domain error: \fIx\fP a negative integer, or negative infinity
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.\" FIXME . errno is not set to EDOM for x == -inf
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.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6809
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.I errno
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is set to
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.BR EDOM .
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An invalid floating-point exception
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.RB ( FE_INVALID )
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is raised (but see BUGS).
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.TP
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Pole error: \fIx\fP is +0 or \-0
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.I errno
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is set to
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.BR ERANGE .
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A divide-by-zero floating-point exception
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.RB ( FE_DIVBYZERO )
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is raised.
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.TP
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Range error: result overflow
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.I errno
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is set to
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.BR ERANGE .
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An overflow floating-point exception
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.RB ( FE_OVERFLOW )
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is raised.
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.PP
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glibc also gives the following error which is not specified
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C99 or POSIX.1-2001.
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.TP
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Range error: result underflow
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.\" e.g., tgamma(-172.5) on glibc 2.8/x86-32
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.\" .I errno
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.\" is set to
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.\" .BR ERANGE .
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An underflow floating-point exception
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.RB ( FE_UNDERFLOW )
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is raised.
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.IP
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.I errno
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is not set for this case.
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.\" FIXME . Is it intentional that errno is not set:
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.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6810
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.\"
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.\" glibc (as at 2.8) also supports and an inexact
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.\" exception for various cases.
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.SH "CONFORMING TO"
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C99, POSIX.1-2001.
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.SH NOTES
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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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.BR gamma (3)
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that returns something else (see
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.BR gamma (3)
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for details).
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.SH BUGS
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If
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.I x
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is negative infinity,
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.I errno
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is not set (it should be set to
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.BE EDOM ).
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.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6809
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.SH "SEE ALSO"
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.BR gamma (3),
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.BR lgamma (3)
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