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32.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92
33.\" $FreeBSD: src/lib/msun/man/lgamma.3,v 1.22 2005/01/16 16:46:14 ru Exp $
34.\"
35.Dd January 14, 2005
36.Dt LGAMMA 3
37.Os
38.Sh NAME
39.Nm lgamma ,
40.Nm lgamma_r ,
41.Nm lgammaf ,
42.Nm lgammaf_r ,
43.Nm gamma ,
44.Nm gamma_r ,
45.Nm gammaf ,
46.Nm gammaf_r ,
47.Nm tgamma
48.Nd log gamma functions, gamma function
49.Sh LIBRARY
50.Lb libm
51.Sh SYNOPSIS
52.In math.h
53.Ft extern int
54.Fa signgam ;
55.sp
56.Ft double
57.Fn lgamma "double x"
58.Ft double
59.Fn lgamma_r "double x" "int *signgamp"
60.Ft float
61.Fn lgammaf "float x"
62.Ft float
63.Fn lgammaf_r "float x" "int *signgamp"
64.Ft double
65.Fn gamma "double x"
66.Ft double
67.Fn gamma_r "double x" "int *signgamp"
68.Ft float
69.Fn gammaf "float x"
70.Ft float
71.Fn gammaf_r "float x" "int *signgamp"
72.Ft double
73.Fn tgamma "double x"
74.Sh DESCRIPTION
75.Fn lgamma x
76and
77.Fn lgammaf x
78.if t \{\
79return ln\||\(*G(x)| where
80.Bd -unfilled -offset indent
81\(*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
82\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1.
83.Ed
84.\}
85.if n \
86return ln\||\(*G(x)|.
87.Pp
88The external integer
89.Fa signgam
90returns the sign of \(*G(x).
91.Pp
92.Fn lgamma_r x signgamp
93and
94.Fn lgammaf_r x signgamp
95provide the same functionality as
96.Fn lgamma x
97and
98.Fn lgammaf x
99but the caller must provide an integer to store the sign of \(*G(x).
100.Pp
101.Fn gamma ,
102.Fn gammaf ,
103.Fn gamma_r ,
104and
105.Fn gammaf_r
106are deprecated aliases for
107.Fn lgamma ,
108.Fn lgammaf ,
109.Fn lgamma_r ,
110and
111.Fn lgammaf_r ,
112respectively.
113.Fn tgamma x
114returns \(*G(x), with no effect on
115.Fa signgam .
116.Sh IDIOSYNCRASIES
117Do not use the expression
118.Dq Li signgam\(**exp(lgamma(x))
119to compute g := \(*G(x).
120Instead use a program like this (in C):
121.Bd -literal -offset indent
122lg = lgamma(x); g = signgam\(**exp(lg);
123.Ed
124.Pp
125Only after
126.Fn lgamma
127or
128.Fn lgammaf
129has returned can signgam be correct.
130.Pp
131For arguments in its range,
132.Fn tgamma
133is preferred, as for positive arguments
134it is accurate to within one unit in the last place.
135Exponentiation of
136.Fn lgamma
137will lose up to 10 significant bits.
138.Sh RETURN VALUES
139.Fn gamma ,
140.Fn gamma_r ,
141.Fn gammaf ,
142.Fn gammaf_r ,
143.Fn lgamma ,
144.Fn lgamma_r ,
145.Fn lgammaf ,
146and
147.Fn lgammaf_r
148return appropriate values unless an argument is out of range.
149Overflow will occur for sufficiently large positive values, and
150non-positive integers.
151For large non-integer negative values,
152.Fn tgamma
153will underflow.
154.Sh SEE ALSO
155.Xr math 3
156.Sh STANDARDS
157The
158.Fn lgamma
159and
160.Fn tgamma
161functions are expected to conform to
162.St -isoC-99 .
163.Sh HISTORY
164The
165.Fn lgamma
166function appeared in
167.Bx 4.3 .
168The
169.Fn gamma
170function appeared in
171.Bx 4.4
172as a function which computed \(*G(x).
173This version was used in
174.Fx 1.1 .
175The name
176.Fn gamma
177was originally dedicated to the
178.Fn lgamma
179function,
180and that usage was restored by switching to Sun's fdlibm in
181.Fx 1.1.5 .
182The
183.Fn tgamma
184function appeared in
185.Fx 5.0 .