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.Dd March 1, 2024
.Dt LGAMMA 3
.Os
.Sh NAME
.Nm lgamma ,
.Nm lgamma_r ,
.Nm lgammaf ,
.Nm lgammaf_r ,
.Nm lgammal ,
.Nm lgammal_r ,
.Nm gamma ,
.Nm gamma_r ,
.Nm gammaf ,
.Nm gammaf_r ,
.Nm tgamma ,
.Nm tgammaf ,
.Nm tgammal ,
.Nd log gamma functions, gamma function
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In math.h
.Ft extern int
.Fa signgam ;
.sp
.Ft double
.Fn lgamma "double x"
.Ft double
.Fn lgamma_r "double x" "int *signgamp"
.Ft float
.Fn lgammaf "float x"
.Ft float
.Fn lgammaf_r "float x" "int *signgamp"
.Ft "long double"
.Fn lgammal "long double x"
.Ft "long double"
.Fn lgammal_r "long double x" "int *signgamp"
.Ft double
.Fn gamma "double x"
.Ft double
.Fn gamma_r "double x" "int *signgamp"
.Ft float
.Fn gammaf "float x"
.Ft float
.Fn gammaf_r "float x" "int *signgamp"
.Ft "long double"
.Fn tgamma "double x"
.Ft float
.Fn tgammaf "float x"
.Ft "long double"
.Fn tgammal "long double x"
.Sh DESCRIPTION
.Fn lgamma x ,
.Fn lgammaf x ,
and
.Fn lgammal x
.if t \{\
return ln\||\(*G(x)| where
.Bd -unfilled -offset indent
\(*G(x) = \(is\d\s8\z0\s10\u\u\s8\(if\s10\d t\u\s8x\-1\s10\d e\u\s8\-t\s10\d dt	for x > 0 and
\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px))	for x < 1.
.Ed
.\}
.if n \
return ln\||\(*G(x)|.
The external integer
.Fa signgam
returns the sign of \(*G(x).
.Pp
.Fn lgamma_r x signgamp ,
.Fn lgammaf_r x signgamp ,
and
.Fn lgammal_r x signgamp
provide the same functionality as
.Fn lgamma x ,
.Fn lgammaf x ,
and
.Fn lgammal x ,
but the caller must provide an integer to store the sign of \(*G(x).
.Pp
The
.Fn tgamma x ,
.Fn tgammaf x ,
and
.Fn tgammal x
functions return \(*G(x), with no effect on
.Fa signgam .
.Pp
.Fn gamma ,
.Fn gammaf ,
.Fn gamma_r ,
and
.Fn gammaf_r
are deprecated aliases for
.Fn lgamma ,
.Fn lgammaf ,
.Fn lgamma_r ,
and
.Fn lgammaf_r ,
respectively.
.Sh IDIOSYNCRASIES
Do not use the expression
.Dq Li signgam\(**exp(lgamma(x))
to compute g := \(*G(x).
Instead use a program like this (in C):
.Bd -literal -offset indent
lg = lgamma(x); g = signgam\(**exp(lg);
.Ed
.Pp
Only after
.Fn lgamma
or
.Fn lgammaf
has returned can signgam be correct.
.Pp
For arguments in its range,
.Fn tgamma
is preferred, as for positive arguments
it is accurate to within one unit in the last place.
Exponentiation of
.Fn lgamma
will lose up to 10 significant bits.
.Sh RETURN VALUES
.Fn gamma ,
.Fn gammaf ,
.Fn gammal ,
.Fn gamma_r ,
.Fn gammaf_r ,
.Fn gammal_r ,
.Fn lgamma ,
.Fn lgammaf ,
.Fn lgammal ,
.Fn lgamma_r ,
.Fn lgammaf_r ,
and
.Fn lgammal_r
return appropriate values unless an argument is out of range.
Overflow will occur for sufficiently large positive values, and
non-positive integers.
For large non-integer negative values,
.Fn tgamma
will underflow.
.Sh SEE ALSO
.Xr math 3
.Sh STANDARDS
The
.Fn lgamma ,
.Fn lgammaf ,
.Fn lgammal ,
.Fn tgamma ,
.Fn tgammaf ,
and
.Fn tgammal
functions are expected to conform to
.St -isoC-99 .
.Sh HISTORY
The
.Fn lgamma
function appeared in
.Bx 4.3 .
The
.Fn gamma
function appeared in
.Bx 4.4
as a function which computed \(*G(x).
This version was used in
.Fx 1.1 .
The name
.Fn gamma
was originally dedicated to the
.Fn lgamma
function,
and that usage was restored by switching to Sun's fdlibm in
.Fx 1.1.5 .
The
.Fn tgamma
function appeared in
.Fx 5.0 .
The 128-bit
.Ft long double
version of
.Fn tgammal
replaced the 80-bit stub version in
version in
.Fx 16 ,
thanks to an appropriate implementation from Arm.