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.
--- 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 271651 2014-09-15 23:21:57Z kargl $
30.\"
31.Dd September 12, 2014
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 lgammal ,
40.Nm lgammal_r ,
41.Nm gamma ,
42.Nm gamma_r ,
43.Nm gammaf ,
44.Nm gammaf_r ,
45.Nm tgamma ,
46.Nm tgammaf
47.Nd log gamma functions, gamma function
48.Sh LIBRARY
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55.Ft double
56.Fn lgamma "double x"
57.Ft double
58.Fn lgamma_r "double x" "int *signgamp"
59.Ft float
60.Fn lgammaf "float x"
61.Ft float
62.Fn lgammaf_r "float x" "int *signgamp"
63.Ft "long double"
64.Fn lgammal "long double x"
65.Ft "long double"
66.Fn lgammal_r "long double x" "int *signgamp"
67.Ft double
68.Fn gamma "double x"
69.Ft double
70.Fn gamma_r "double x" "int *signgamp"
71.Ft float
72.Fn gammaf "float x"
73.Ft float
74.Fn gammaf_r "float x" "int *signgamp"
75.Ft "long double"
76.Fn tgamma "double x"
77.Ft float
78.Fn tgammaf "float x"
79.Sh DESCRIPTION
80.Fn lgamma x ,
81.Fn lgammaf x ,
82and
83.Fn lgammal x
84.if t \{\
85return ln\||\(*G(x)| where
86.Bd -unfilled -offset indent
87\(*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
88\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1.
89.Ed
90.\}
91.if n \
92return ln\||\(*G(x)|.
93The external integer
94.Fa signgam
95returns the sign of \(*G(x).
96.Pp
97.Fn lgamma_r x signgamp ,
98.Fn lgammaf_r x signgamp ,
99and
100.Fn lgammal_r x signgamp
101provide the same functionality as
102.Fn lgamma x ,
103.Fn lgammaf x ,
104and
105.Fn lgammal x ,
106but the caller must provide an integer to store the sign of \(*G(x).
107.Pp
108The
109.Fn tgamma x
110and
111.Fn tgammaf x
112functions return \(*G(x), with no effect on
113.Fa signgam .
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119.Fn gammaf_r
120are deprecated aliases for
121.Fn lgamma ,
122.Fn lgammaf ,
123.Fn lgamma_r ,
124and
125.Fn lgammaf_r ,
126respectively.
127
128.Sh IDIOSYNCRASIES
129Do not use the expression
130.Dq Li signgam\(**exp(lgamma(x))
131to compute g := \(*G(x).
132Instead use a program like this (in C):
133.Bd -literal -offset indent
134lg = lgamma(x); g = signgam\(**exp(lg);
135.Ed
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144.Fn tgamma
145is preferred, as for positive arguments
146it is accurate to within one unit in the last place.
147Exponentiation of
148.Fn lgamma
149will lose up to 10 significant bits.
150.Sh RETURN VALUES
151.Fn gamma ,
152.Fn gammaf ,
153.Fn gammal ,
154.Fn gamma_r ,
155.Fn gammaf_r ,
156.Fn gammal_r ,
157.Fn lgamma ,
158.Fn lgammaf ,
159.Fn lgammal ,
160.Fn lgamma_r ,
161.Fn lgammaf_r ,
162and
163.Fn lgammal_r
164return appropriate values unless an argument is out of range.
165Overflow will occur for sufficiently large positive values, and
166non-positive integers.
167For large non-integer negative values,
168.Fn tgamma
169will underflow.
170.Sh SEE ALSO
171.Xr math 3
172.Sh STANDARDS
173The
174.Fn lgamma ,
175.Fn lgammaf ,
176.Fn lgammal ,
177.Fn tgamma ,
178and
179.Fn tgammaf
180functions are expected to conform to
181.St -isoC-99 .
182.Sh HISTORY
183The
184.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 271651 2014-09-15 23:21:57Z kargl $
30.\"
31.Dd September 12, 2014
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 lgammal ,
40.Nm lgammal_r ,
41.Nm gamma ,
42.Nm gamma_r ,
43.Nm gammaf ,
44.Nm gammaf_r ,
45.Nm tgamma ,
46.Nm tgammaf
47.Nd log gamma functions, gamma function
48.Sh LIBRARY
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55.Ft double
56.Fn lgamma "double x"
57.Ft double
58.Fn lgamma_r "double x" "int *signgamp"
59.Ft float
60.Fn lgammaf "float x"
61.Ft float
62.Fn lgammaf_r "float x" "int *signgamp"
63.Ft "long double"
64.Fn lgammal "long double x"
65.Ft "long double"
66.Fn lgammal_r "long double x" "int *signgamp"
67.Ft double
68.Fn gamma "double x"
69.Ft double
70.Fn gamma_r "double x" "int *signgamp"
71.Ft float
72.Fn gammaf "float x"
73.Ft float
74.Fn gammaf_r "float x" "int *signgamp"
75.Ft "long double"
76.Fn tgamma "double x"
77.Ft float
78.Fn tgammaf "float x"
79.Sh DESCRIPTION
80.Fn lgamma x ,
81.Fn lgammaf x ,
82and
83.Fn lgammal x
84.if t \{\
85return ln\||\(*G(x)| where
86.Bd -unfilled -offset indent
87\(*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
88\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1.
89.Ed
90.\}
91.if n \
92return ln\||\(*G(x)|.
93The external integer
94.Fa signgam
95returns the sign of \(*G(x).
96.Pp
97.Fn lgamma_r x signgamp ,
98.Fn lgammaf_r x signgamp ,
99and
100.Fn lgammal_r x signgamp
101provide the same functionality as
102.Fn lgamma x ,
103.Fn lgammaf x ,
104and
105.Fn lgammal x ,
106but the caller must provide an integer to store the sign of \(*G(x).
107.Pp
108The
109.Fn tgamma x
110and
111.Fn tgammaf x
112functions return \(*G(x), with no effect on
113.Fa signgam .
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119.Fn gammaf_r
120are deprecated aliases for
121.Fn lgamma ,
122.Fn lgammaf ,
123.Fn lgamma_r ,
124and
125.Fn lgammaf_r ,
126respectively.
127
128.Sh IDIOSYNCRASIES
129Do not use the expression
130.Dq Li signgam\(**exp(lgamma(x))
131to compute g := \(*G(x).
132Instead use a program like this (in C):
133.Bd -literal -offset indent
134lg = lgamma(x); g = signgam\(**exp(lg);
135.Ed
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144.Fn tgamma
145is preferred, as for positive arguments
146it is accurate to within one unit in the last place.
147Exponentiation of
148.Fn lgamma
149will lose up to 10 significant bits.
150.Sh RETURN VALUES
151.Fn gamma ,
152.Fn gammaf ,
153.Fn gammal ,
154.Fn gamma_r ,
155.Fn gammaf_r ,
156.Fn gammal_r ,
157.Fn lgamma ,
158.Fn lgammaf ,
159.Fn lgammal ,
160.Fn lgamma_r ,
161.Fn lgammaf_r ,
162and
163.Fn lgammal_r
164return appropriate values unless an argument is out of range.
165Overflow will occur for sufficiently large positive values, and
166non-positive integers.
167For large non-integer negative values,
168.Fn tgamma
169will underflow.
170.Sh SEE ALSO
171.Xr math 3
172.Sh STANDARDS
173The
174.Fn lgamma ,
175.Fn lgammaf ,
176.Fn lgammal ,
177.Fn tgamma ,
178and
179.Fn tgammaf
180functions are expected to conform to
181.St -isoC-99 .
182.Sh HISTORY
183The
184.Fn lgamma
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