1.\" Copyright (c) 1985, 1991 Regents of the University of California.
2.\" All rights reserved.
3.\"
4.\" Redistribution and use in source and binary forms, with or without
5.\" modification, are permitted provided that the following conditions
6.\" are met:
7.\" 1. Redistributions of source code must retain the above copyright
8.\" notice, this list of conditions and the following disclaimer.
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21.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
22.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
23.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
24.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
25.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
26.\" SUCH DAMAGE.
27.\"
28.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92
29.\" $FreeBSD: head/lib/msun/man/lgamma.3 176388 2008-02-18 17:27:11Z das $
30.\"
31.Dd January 14, 2005
32.Dt LGAMMA 3
33.Os
34.Sh NAME
35.Nm lgamma ,
36.Nm lgamma_r ,
37.Nm lgammaf ,
38.Nm lgammaf_r ,
39.Nm gamma ,
40.Nm gamma_r ,
41.Nm gammaf ,
42.Nm gammaf_r ,
43.Nm tgamma ,
44.Nm tgammaf
45.Nd log gamma functions, gamma function
46.Sh LIBRARY
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53.Ft double
54.Fn lgamma "double x"
55.Ft double
56.Fn lgamma_r "double x" "int *signgamp"
57.Ft float
58.Fn lgammaf "float x"
59.Ft float
60.Fn lgammaf_r "float x" "int *signgamp"
61.Ft double
62.Fn gamma "double x"
63.Ft double
64.Fn gamma_r "double x" "int *signgamp"
65.Ft float
66.Fn gammaf "float x"
67.Ft float
68.Fn gammaf_r "float x" "int *signgamp"
69.Ft double
70.Fn tgamma "double x"
71.Ft float
72.Fn tgammaf "float x"
73.Sh DESCRIPTION
74.Fn lgamma x
75and
76.Fn lgammaf x
77.if t \{\
78return ln\||\(*G(x)| where
79.Bd -unfilled -offset indent
80\(*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
81\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1.
82.Ed
83.\}
84.if n \
85return ln\||\(*G(x)|.
86The external integer
87.Fa signgam
88returns the sign of \(*G(x).
89.Pp
90.Fn lgamma_r x signgamp
91and
92.Fn lgammaf_r x signgamp
93provide the same functionality as
94.Fn lgamma x
95and
96.Fn lgammaf x
97but the caller must provide an integer to store the sign of \(*G(x).
98.Pp
99The
100.Fn tgamma x
101and
102.Fn tgammaf x
103functions return \(*G(x), with no effect on
104.Fa signgam .
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110.Fn gammaf_r
111are deprecated aliases for
112.Fn lgamma ,
113.Fn lgammaf ,
114.Fn lgamma_r ,
115and
116.Fn lgammaf_r ,
117respectively.
118.Sh IDIOSYNCRASIES
119Do not use the expression
120.Dq Li signgam\(**exp(lgamma(x))
121to compute g := \(*G(x).
122Instead use a program like this (in C):
123.Bd -literal -offset indent
124lg = lgamma(x); g = signgam\(**exp(lg);
125.Ed
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134.Fn tgamma
135is preferred, as for positive arguments
136it is accurate to within one unit in the last place.
137Exponentiation of
138.Fn lgamma
139will lose up to 10 significant bits.
140.Sh RETURN VALUES
141.Fn gamma ,
142.Fn gamma_r ,
143.Fn gammaf ,
144.Fn gammaf_r ,
145.Fn lgamma ,
146.Fn lgamma_r ,
147.Fn lgammaf ,
148and
149.Fn lgammaf_r
150return appropriate values unless an argument is out of range.
151Overflow will occur for sufficiently large positive values, and
152non-positive integers.
153For large non-integer negative values,
154.Fn tgamma
155will underflow.
156.Sh SEE ALSO
157.Xr math 3
158.Sh STANDARDS
159The
160.Fn lgamma ,
161.Fn lgammaf ,
162.Fn tgamma ,
163and
164.Fn tgammaf
165functions are expected to conform to
166.St -isoC-99 .
167.Sh HISTORY
168The
169.Fn lgamma
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2.\" All rights reserved.
3.\"
4.\" Redistribution and use in source and binary forms, with or without
5.\" modification, are permitted provided that the following conditions
6.\" are met:
7.\" 1. Redistributions of source code must retain the above copyright
8.\" notice, this list of conditions and the following disclaimer.
--- 12 unchanged lines hidden (view full) ---
21.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
22.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
23.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
24.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
25.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
26.\" SUCH DAMAGE.
27.\"
28.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92
29.\" $FreeBSD: head/lib/msun/man/lgamma.3 176388 2008-02-18 17:27:11Z das $
30.\"
31.Dd January 14, 2005
32.Dt LGAMMA 3
33.Os
34.Sh NAME
35.Nm lgamma ,
36.Nm lgamma_r ,
37.Nm lgammaf ,
38.Nm lgammaf_r ,
39.Nm gamma ,
40.Nm gamma_r ,
41.Nm gammaf ,
42.Nm gammaf_r ,
43.Nm tgamma ,
44.Nm tgammaf
45.Nd log gamma functions, gamma function
46.Sh LIBRARY
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53.Ft double
54.Fn lgamma "double x"
55.Ft double
56.Fn lgamma_r "double x" "int *signgamp"
57.Ft float
58.Fn lgammaf "float x"
59.Ft float
60.Fn lgammaf_r "float x" "int *signgamp"
61.Ft double
62.Fn gamma "double x"
63.Ft double
64.Fn gamma_r "double x" "int *signgamp"
65.Ft float
66.Fn gammaf "float x"
67.Ft float
68.Fn gammaf_r "float x" "int *signgamp"
69.Ft double
70.Fn tgamma "double x"
71.Ft float
72.Fn tgammaf "float x"
73.Sh DESCRIPTION
74.Fn lgamma x
75and
76.Fn lgammaf x
77.if t \{\
78return ln\||\(*G(x)| where
79.Bd -unfilled -offset indent
80\(*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
81\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1.
82.Ed
83.\}
84.if n \
85return ln\||\(*G(x)|.
86The external integer
87.Fa signgam
88returns the sign of \(*G(x).
89.Pp
90.Fn lgamma_r x signgamp
91and
92.Fn lgammaf_r x signgamp
93provide the same functionality as
94.Fn lgamma x
95and
96.Fn lgammaf x
97but the caller must provide an integer to store the sign of \(*G(x).
98.Pp
99The
100.Fn tgamma x
101and
102.Fn tgammaf x
103functions return \(*G(x), with no effect on
104.Fa signgam .
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110.Fn gammaf_r
111are deprecated aliases for
112.Fn lgamma ,
113.Fn lgammaf ,
114.Fn lgamma_r ,
115and
116.Fn lgammaf_r ,
117respectively.
118.Sh IDIOSYNCRASIES
119Do not use the expression
120.Dq Li signgam\(**exp(lgamma(x))
121to compute g := \(*G(x).
122Instead use a program like this (in C):
123.Bd -literal -offset indent
124lg = lgamma(x); g = signgam\(**exp(lg);
125.Ed
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134.Fn tgamma
135is preferred, as for positive arguments
136it is accurate to within one unit in the last place.
137Exponentiation of
138.Fn lgamma
139will lose up to 10 significant bits.
140.Sh RETURN VALUES
141.Fn gamma ,
142.Fn gamma_r ,
143.Fn gammaf ,
144.Fn gammaf_r ,
145.Fn lgamma ,
146.Fn lgamma_r ,
147.Fn lgammaf ,
148and
149.Fn lgammaf_r
150return appropriate values unless an argument is out of range.
151Overflow will occur for sufficiently large positive values, and
152non-positive integers.
153For large non-integer negative values,
154.Fn tgamma
155will underflow.
156.Sh SEE ALSO
157.Xr math 3
158.Sh STANDARDS
159The
160.Fn lgamma ,
161.Fn lgammaf ,
162.Fn tgamma ,
163and
164.Fn tgammaf
165functions are expected to conform to
166.St -isoC-99 .
167.Sh HISTORY
168The
169.Fn lgamma
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