1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
|
.\" $OpenBSD: lgamma.3,v 1.22 2015/01/15 19:06:31 schwarze Exp $
.\" Copyright (c) 1985, 1991 Regents of the University of California.
.\" All rights reserved.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions
.\" are met:
.\" 1. Redistributions of source code must retain the above copyright
.\" notice, this list of conditions and the following disclaimer.
.\" 2. Redistributions in binary form must reproduce the above copyright
.\" notice, this list of conditions and the following disclaimer in the
.\" documentation and/or other materials provided with the distribution.
.\" 3. Neither the name of the University nor the names of its contributors
.\" may be used to endorse or promote products derived from this software
.\" without specific prior written permission.
.\"
.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
.\" SUCH DAMAGE.
.\"
.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92
.\"
.Dd $Mdocdate: January 15 2015 $
.Dt LGAMMA 3
.Os
.Sh NAME
.Nm lgamma ,
.Nm lgammaf ,
.Nm lgammal ,
.Nm lgamma_r ,
.Nm lgammaf_r ,
.Nm lgammal_r ,
.Nm tgamma ,
.Nm tgammaf ,
.Nm tgammal
.Nd log gamma functions
.Sh SYNOPSIS
.In math.h
.Ft extern int
.Fa signgam ;
.sp
.Ft double
.Fn lgamma "double x"
.Ft float
.Fn lgammaf "float x"
.Ft long double
.Fn lgammal "long double x"
.Ft double
.Fn lgamma_r "double x" "int *signgamp"
.Ft float
.Fn lgammaf_r "float x" "int *signgamp"
.Ft long double
.Fn lgammal_r "long double x" "int *signgamp"
.Ft double
.Fn tgamma "double x"
.Ft float
.Fn tgammaf "float x"
.Ft long double
.Fn tgammal "long double x"
.Sh DESCRIPTION
.Fn lgamma x
.if t \{\
returns 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
.br
\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1.
.Ed
.\}
.if n \
returns ln\||\(*G(x)|.
.Pp
The external integer
.Fa signgam
returns the sign of \(*G(x).
The
.Fn lgammaf
function is a single precision version of
.Fn lgamma .
The
.Fn lgammal
function is an extended precision version of
.Fn lgamma .
.Pp
The
.Fn lgamma_r ,
.Fn lgammaf_r ,
and
.Fn lgammal_r
functions are thread-safe versions of
.Fn lgamma ,
.Fn lgammaf ,
and
.Fn lgammal
that return the sign via the
.Fa signgamp
pointer instead of modifying
.Fa signgam .
.Pp
The
.Fn tgamma x ,
.Fn tgammaf x
and
.Fn tgammal x
functions return \(*G(x), with no effect on
.Fa signgam .
.Sh IDIOSYNCRASIES
Do not use the expression
.Sq 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
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.
.Sh RETURN VALUES
.Fn lgamma
returns 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.
On the VAX, the reserved operator is returned, and
.Va errno
is set to
.Er ERANGE .
.Sh SEE ALSO
.Xr infnan 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 .
.Pp
The
.Fn lgamma_r ,
.Fn lgammaf_r ,
and
.Fn lgammal_r
functions are
.Bx
extensions.
.Pp
.Fn gamma
and
.Fn gammaf
are deprecated aliases for
.Fn lgamma
and
.Fn lgammaf ,
respectively.
.Sh HISTORY
A
.Fn gamma
function first appeared in
.At v5 .
The
.Fn lgamma
function first appeared in
.Bx 4.3 .
The
.Fn tgamma
function first appeared in
.Ox 4.4 ,
and is based on the
.Fn gamma
function that appeared in
.Bx 4.4
as a function to compute \(*G(x).
|
