.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
+.\"
+.\" %%%LICENSE_START(GPL_NOVERSION_ONELINE)
.\" Distributed under GPL
+.\" %%%LICENSE_END
+.\"
.\" Based on glibc infopages
.\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk
.\" <mtk.manpages@gmail.com>
.\" Modified 2004-11-15, fixed error noted by Fabian Kreutz
.\" <kreutz@dbs.uni-hannover.de>
-.TH TGAMMA 3 2008-08-11 "GNU" "Linux Programmer's Manual"
+.\"
+.TH TGAMMA 3 2017-09-15 "GNU" "Linux Programmer's Manual"
.SH NAME
tgamma, tgammaf, tgammal \- true gamma function
.SH SYNOPSIS
.B #include <math.h>
-.sp
+.PP
.BI "double tgamma(double " x );
.br
.BI "float tgammaf(float " x );
.br
.BI "long double tgammal(long double " x );
-.sp
+.PP
Link with \fI\-lm\fP.
-.sp
+.PP
.in -4n
Feature Test Macro Requirements for glibc (see
.BR feature_test_macros (7)):
.in
-.sp
+.PP
.ad l
.BR tgamma (),
.BR tgammaf (),
.BR tgammal ():
-_XOPEN_SOURCE\ >=\ 600 || _ISOC99_SOURCE; or
-.I cc\ -std=c99
-.ad b
+.RS 4
+_ISOC99_SOURCE ||
+_POSIX_C_SOURCE\ >=\ 200112L
+.RE
+.ad
.SH DESCRIPTION
+These functions calculate the Gamma function of
+.IR x .
+.PP
The Gamma function is defined by
-.sp
- Gamma(x) = integral from 0 to infinity of t^(x\-1) e^\-t dt
-.sp
-It is defined for every real number except for non-positive integers.
-For non-negative integral \fIm\fP one has
-.sp
- Gamma(m+1) = m!
-.sp
-and, more generally, for all \fIx\fP:
-.sp
- Gamma(x+1) = x * Gamma(x)
-.sp
-Furthermore, the following is valid for all values of \fIx\fP
+.PP
+.RS
+Gamma(x) = integral from 0 to infinity of t^(x\-1) e^\-t dt
+.RE
+.PP
+It is defined for every real number except for nonpositive integers.
+For nonnegative integral
+.I m
+one has
+.PP
+.RS
+Gamma(m+1) = m!
+.RE
+.PP
+and, more generally, for all
+.IR x :
+.PP
+.RS
+Gamma(x+1) = x * Gamma(x)
+.RE
+.PP
+Furthermore, the following is valid for all values of
+.I x
outside the poles:
-.sp
- Gamma(x) * Gamma(1 \- x) = PI / sin(PI * x)
.PP
+.RS
+Gamma(x) * Gamma(1 \- x) = PI / sin(PI * x)
+.RE
.SH RETURN VALUE
On success, these functions return Gamma(x).
-
+.PP
If
.I x
is a NaN, a NaN is returned.
-
+.PP
If
.I x
is positive infinity, positive infinity is returned.
-
+.PP
If
.I x
is a negative integer, or is negative infinity,
a domain error occurs,
and a NaN is returned.
-
+.PP
If the result overflows,
a range error occurs,
and the functions return
or
.BR HUGE_VALL ,
respectively, with the correct mathematical sign.
-
+.PP
If the result underflows,
a range error occurs,
and the functions return 0, with the correct mathematical sign.
-
+.PP
If
.I x
-is -0 or +0,
+is \-0 or +0,
a pole error occurs,
and the functions return
.BR HUGE_VAL ,
The following errors can occur:
.TP
Domain error: \fIx\fP is a negative integer, or negative infinity
-.\" FIXME . errno is not set to EDOM for x == -inf
-.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6809
.I errno
is set to
.BR EDOM .
.\" .BR ERANGE .
An underflow floating-point exception
.RB ( FE_UNDERFLOW )
-is raised.
-.IP
+is raised, and
.I errno
-is not set for this case.
-.\" FIXME . Is it intentional that errno is not set:
-.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6810
-.\"
-.\" glibc (as at 2.8) also supports and an inexact
+is set to
+.BR ERANGE .
+.\" glibc (as at 2.8) also supports an inexact
.\" exception for various cases.
.SH VERSIONS
These functions first appeared in glibc in version 2.1.
-.SH "CONFORMING TO"
-C99, POSIX.1-2001.
+.SH ATTRIBUTES
+For an explanation of the terms used in this section, see
+.BR attributes (7).
+.TS
+allbox;
+lbw30 lb lb
+l l l.
+Interface Attribute Value
+T{
+.BR tgamma (),
+.BR tgammaf (),
+.BR tgammal ()
+T} Thread safety MT-Safe
+.TE
+.SH CONFORMING TO
+C99, POSIX.1-2001, POSIX.1-2008.
.SH NOTES
This function had to be called "true gamma function"
since there is already a function
.BR gamma (3)
for details).
.SH BUGS
-If
+Before version 2.18, the glibc implementation of these functions did not set
+.\" http://sources.redhat.com/bugzilla/show_bug.cgi?id=6809
+.I errno
+to
+.B EDOM
+when
.I x
-is negative infinity,
+is negative infinity.
+.PP
+Before glibc 2.19,
+.\" http://sources.redhat.com/bugzilla/show_bug.cgi?id=6810
+the glibc implementation of these functions did not set
.I errno
-is not set (it should be set to
-.BR EDOM ).
-.\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6809
-
+to
+.B ERANGE
+on an underflow range error.
+.I x
+.PP
+.\"
In glibc versions 2.3.3 and earlier,
-an argument of +0 or -0 incorrectly produced a domain error
+an argument of +0 or \-0 incorrectly produced a domain error
.RI ( errno
set to
.B EDOM
and an
.B FE_INVALID
exception raised), rather than a pole error.
-.SH "SEE ALSO"
+.SH SEE ALSO
.BR gamma (3),
.BR lgamma (3)
projects / thirdparty / man-pages.git / blobdiff