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
193
194
195
196
197
198
199
200
201
202
|
.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
.\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk
.\" <mtk.manpages@gmail.com>
.\"
.\" SPDX-License-Identifier: GPL-1.0-or-later
.\"
.\" based on glibc infopages
.\"
.TH lgamma 3 2023-03-30 "Linux man-pages 6.05.01"
.SH NAME
lgamma, lgammaf, lgammal, lgamma_r, lgammaf_r, lgammal_r, signgam \-
log gamma function
.SH LIBRARY
Math library
.RI ( libm ", " \-lm )
.SH SYNOPSIS
.nf
.B #include <math.h>
.PP
.BI "double lgamma(double " x );
.BI "float lgammaf(float " x );
.BI "long double lgammal(long double " x );
.PP
.BI "double lgamma_r(double " x ", int *" signp );
.BI "float lgammaf_r(float " x ", int *" signp );
.BI "long double lgammal_r(long double " x ", int *" signp );
.PP
.BI "extern int " signgam ;
.fi
.PP
.RS -4
Feature Test Macro Requirements for glibc (see
.BR feature_test_macros (7)):
.RE
.PP
.nf
.BR lgamma ():
_ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L || _XOPEN_SOURCE
|| /* Since glibc 2.19: */ _DEFAULT_SOURCE
|| /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
.fi
.PP
.BR lgammaf (),
.BR lgammal ():
.nf
_ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
|| /* Since glibc 2.19: */ _DEFAULT_SOURCE
|| /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
.fi
.PP
.BR lgamma_r (),
.BR lgammaf_r (),
.BR lgammal_r ():
.nf
/* Since glibc 2.19: */ _DEFAULT_SOURCE
|| /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
.fi
.PP
.IR signgam :
.nf
_XOPEN_SOURCE
|| /* Since glibc 2.19: */ _DEFAULT_SOURCE
|| /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
.fi
.SH DESCRIPTION
For the definition of the Gamma function, see
.BR tgamma (3).
.PP
The
.BR lgamma (),
.BR lgammaf (),
and
.BR lgammal ()
functions return the natural logarithm of
the absolute value of the Gamma function.
The sign of the Gamma function is returned in the
external integer
.I signgam
declared in
.IR <math.h> .
It is 1 when the Gamma function is positive or zero, \-1
when it is negative.
.PP
Since using a constant location
.I signgam
is not thread-safe, the functions
.BR lgamma_r (),
.BR lgammaf_r (),
and
.BR lgammal_r ()
have been introduced; they return the sign via the argument
.IR signp .
.SH RETURN VALUE
On success, these functions return the natural logarithm of Gamma(x).
.PP
If
.I x
is a NaN, a NaN is returned.
.PP
If
.I x
is 1 or 2, +0 is returned.
.PP
If
.I x
is positive infinity or negative infinity,
positive infinity is returned.
.PP
If
.I x
is a nonpositive integer,
a pole error occurs,
and the functions return
.RB + HUGE_VAL ,
.RB + HUGE_VALF ,
or
.RB + HUGE_VALL ,
respectively.
.PP
If the result overflows,
a range error occurs,
.\" e.g., lgamma(DBL_MAX)
and the functions return
.BR HUGE_VAL ,
.BR HUGE_VALF ,
or
.BR HUGE_VALL ,
respectively, with the correct mathematical sign.
.SH ERRORS
See
.BR math_error (7)
for information on how to determine whether an error has occurred
when calling these functions.
.PP
The following errors can occur:
.TP
Pole error: \fIx\fP is a nonpositive integer
.I errno
is set to
.B ERANGE
(but see BUGS).
A divide-by-zero floating-point exception
.RB ( FE_DIVBYZERO )
is raised.
.TP
Range error: result overflow
.I errno
is set to
.BR ERANGE .
An overflow floating-point exception
.RB ( FE_OVERFLOW )
is raised.
.\" glibc (as at 2.8) also supports an inexact
.\" exception for various cases.
.SH STANDARDS
.TP
.BR lgamma ()
.TQ
.BR lgammaf ()
.TQ
.BR lgammal ()
C11, POSIX.1-2008.
.TP
.I signgam
POSIX.1-2008.
.TP
.BR lgamma_r ()
.TQ
.BR lgammaf_r ()
.TQ
.BR lgammal_r ()
None.
.SH HISTORY
.TP
.BR lgamma ()
.TQ
.BR lgammaf ()
.TQ
.BR lgammal ()
C99, POSIX.1-2001.
.TP
.I signgam
POSIX.1-2001.
.TP
.BR lgamma_r ()
.TQ
.BR lgammaf_r ()
.TQ
.BR lgammal_r ()
None.
.SH BUGS
In glibc 2.9 and earlier,
.\" https://www.sourceware.org/bugzilla/show_bug.cgi?id=6777
when a pole error occurs,
.I errno
is set to
.BR EDOM ;
instead of the POSIX-mandated
.BR ERANGE .
Since glibc 2.10, glibc does the right thing.
.SH SEE ALSO
.BR tgamma (3)
|
