'\" et
.TH TGAMMA "3P" 2017 "IEEE/The Open Group" "POSIX Programmer's Manual"
.\"
.SH PROLOG
This manual page is part of the POSIX Programmer's Manual.
The Linux implementation of this interface may differ (consult
the corresponding Linux manual page for details of Linux behavior),
or the interface may not be implemented on Linux.
.\"
.EQ
delim $$
.EN
.SH NAME
tgamma,
tgammaf,
tgammal
\(em compute gamma(\|) function
.SH SYNOPSIS
.LP
.nf
#include <math.h>
.P
double tgamma(double \fIx\fP);
float tgammaf(float \fIx\fP);
long double tgammal(long double \fIx\fP);
.fi
.SH DESCRIPTION
The functionality described on this reference page is aligned with the
ISO\ C standard. Any conflict between the requirements described here and the
ISO\ C standard is unintentional. This volume of POSIX.1\(hy2017 defers to the ISO\ C standard.
.P
These functions shall compute $\(*G ( ^ x )$
where $\(*G ( ^ x )$ is defined as
$int from 0 to inf e"^" " "{ - t } t"^" " "{ x - 1 } dt$.
.P
An application wishing to check for error situations should set
.IR errno
to zero and call
.IR feclearexcept (FE_ALL_EXCEPT)
before calling these functions. On return, if
.IR errno
is non-zero or \fIfetestexcept\fR(FE_INVALID | FE_DIVBYZERO |
FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.
.SH "RETURN VALUE"
Upon successful completion, these functions shall return the gamma of
.IR x .
.P
If
.IR x
is a negative integer, a
domain
error may occur and either a NaN (if supported) or an
implementation-defined value shall be returned.
On systems that support the IEC 60559 Floating-Point option, a domain
error shall occur and a NaN shall be returned.
.P
If
.IR x
is \(+-0,
\fItgamma\fR(),
\fItgammaf\fR(),
and
\fItgammal\fR()
shall return \(+-HUGE_VAL, \(+-HUGE_VALF, and \(+-HUGE_VALL,
respectively.
On systems that support the IEC 60559 Floating-Point option, a pole
error shall occur;
otherwise, a
pole
error may occur.
.P
If the correct value would cause overflow, a range error shall occur
and
\fItgamma\fR(),
\fItgammaf\fR(),
and
\fItgammal\fR()
shall return \(+-HUGE_VAL, \(+-HUGE_VALF, or \(+-HUGE_VALL,
respectively, with the same sign as the correct value of the function.
.P
If the correct value would cause underflow,
and is not representable,
a range error may occur, and
\fItgamma\fR(),
\fItgammaf\fR(),
and
\fItgammal\fR()
shall return
0.0, or
(if IEC 60559 Floating-Point is not supported) an implementation-defined
value no greater in magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN,
respectively.
.P
If the correct value would cause underflow, and is representable,
a range error may occur and the correct value shall be returned.
.P
If
.IR x
is subnormal and 1/\c
.IR x
is representable, 1/\c
.IR x
should be returned.
.P
If
.IR x
is NaN, a NaN shall be returned.
.P
If
.IR x
is +Inf,
.IR x
shall be returned.
.P
If
.IR x
is \-Inf, a domain error shall occur, and a NaN shall be returned.
.SH ERRORS
These functions shall fail if:
.IP "Domain\ Error" 12
The value of
.IR x
is a negative integer, or
.IR x
is \-Inf.
.RS 12 
.P
If the integer expression (\fImath_errhandling\fR & MATH_ERRNO) is
non-zero, then
.IR errno
shall be set to
.BR [EDOM] .
If the integer expression (\fImath_errhandling\fR & MATH_ERREXCEPT) is
non-zero, then the invalid floating-point exception shall be raised.
.RE
.IP "Pole\ Error" 12
The value of
.IR x
is zero.
.RS 12 
.P
If the integer expression (\fImath_errhandling\fR & MATH_ERRNO) is
non-zero, then
.IR errno
shall be set to
.BR [ERANGE] .
If the integer expression (\fImath_errhandling\fR & MATH_ERREXCEPT) is
non-zero, then the divide-by-zero floating-point exception shall be
raised.
.br
.RE
.IP "Range\ Error" 12
The value overflows.
.RS 12 
.P
If the integer expression (\fImath_errhandling\fR & MATH_ERRNO) is
non-zero, then
.IR errno
shall be set to
.BR [ERANGE] .
If the integer expression (\fImath_errhandling\fR & MATH_ERREXCEPT) is
non-zero, then the overflow floating-point exception shall be raised.
.RE
.P
These functions may fail if:
.IP "Domain\ Error" 12
The value of
.IR x
is a negative integer.
.RS 12 
.P
If the integer expression (\fImath_errhandling\fR & MATH_ERRNO) is
non-zero, then
.IR errno
shall be set to
.BR [EDOM] .
If the integer expression (\fImath_errhandling\fR & MATH_ERREXCEPT) is
non-zero, then the invalid floating-point exception shall be raised.
.RE
.IP "Pole\ Error" 12
The value of
.IR x
is zero.
.RS 12 
.P
If the integer expression (\fImath_errhandling\fR & MATH_ERRNO) is
non-zero, then
.IR errno
shall be set to
.BR [ERANGE] .
If the integer expression (\fImath_errhandling\fR & MATH_ERREXCEPT) is
non-zero, then the divide-by-zero floating-point exception shall be
raised.
.RE
.IP "Range\ Error" 12
The result underflows.
.RS 12 
.P
If the integer expression (\fImath_errhandling\fR & MATH_ERRNO) is
non-zero, then
.IR errno
shall be set to
.BR [ERANGE] .
If the integer expression (\fImath_errhandling\fR & MATH_ERREXCEPT)
is non-zero, then the underflow floating-point exception shall be raised.
.RE
.LP
.IR "The following sections are informative."
.SH EXAMPLES
None.
.SH "APPLICATION USAGE"
On error, the expressions (\fImath_errhandling\fR & MATH_ERRNO) and
(\fImath_errhandling\fR & MATH_ERREXCEPT) are independent of each
other, but at least one of them must be non-zero.
.SH RATIONALE
This function is named
\fItgamma\fR()
in order to avoid conflicts with the historical
.IR gamma (\|)
and
\fIlgamma\fR()
functions.
.SH "FUTURE DIRECTIONS"
It is possible that the error response for a negative integer argument
may be changed to a pole error and a return value of \(+-Inf.
.SH "SEE ALSO"
.IR "\fIfeclearexcept\fR\^(\|)",
.IR "\fIfetestexcept\fR\^(\|)",
.IR "\fIlgamma\fR\^(\|)"
.P
The Base Definitions volume of POSIX.1\(hy2017,
.IR "Section 4.20" ", " "Treatment of Error Conditions for Mathematical Functions",
.IR "\fB<math.h>\fP"
.\"
.SH COPYRIGHT
Portions of this text are reprinted and reproduced in electronic form
from IEEE Std 1003.1-2017, Standard for Information Technology
-- Portable Operating System Interface (POSIX), The Open Group Base
Specifications Issue 7, 2018 Edition,
Copyright (C) 2018 by the Institute of
Electrical and Electronics Engineers, Inc and The Open Group.
In the event of any discrepancy between this version and the original IEEE and
The Open Group Standard, the original IEEE and The Open Group Standard
is the referee document. The original Standard can be obtained online at
http://www.opengroup.org/unix/online.html .
.PP
Any typographical or formatting errors that appear
in this page are most likely
to have been introduced during the conversion of the source files to
man page format. To report such errors, see
https://www.kernel.org/doc/man-pages/reporting_bugs.html .