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
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7.\" 1. Redistributions of source code must retain the above copyright
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9.\" 2. Redistributions in binary form must reproduce the above copyright
10.\" notice, this list of conditions and the following disclaimer in the
11.\" documentation and/or other materials provided with the distribution.
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16.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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25.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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27.\"
28.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92
| 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.
9.\" 2. Redistributions in binary form must reproduce the above copyright
10.\" notice, this list of conditions and the following disclaimer in the
11.\" documentation and/or other materials provided with the distribution.
12.\" 4. Neither the name of the University nor the names of its contributors
13.\" may be used to endorse or promote products derived from this software
14.\" without specific prior written permission.
15.\"
16.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
17.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
18.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
19.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
20.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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 $
| 29.\" $FreeBSD: head/lib/msun/man/lgamma.3 271651 2014-09-15 23:21:57Z kargl $
|
30.\"
| 30.\"
|
31.Dd January 14, 2005
| 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 ,
| 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 ,
|
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
47.Lb libm
48.Sh SYNOPSIS
49.In math.h
50.Ft extern int
51.Fa signgam ;
52.sp
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"
| 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
49.Lb libm
50.Sh SYNOPSIS
51.In math.h
52.Ft extern int
53.Fa signgam ;
54.sp
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"
|
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"
| 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"
|
69.Ft double
| 75.Ft "long double"
|
70.Fn tgamma "double x"
71.Ft float
72.Fn tgammaf "float x"
73.Sh DESCRIPTION
| 76.Fn tgamma "double x"
77.Ft float
78.Fn tgammaf "float x"
79.Sh DESCRIPTION
|
74.Fn lgamma x
| 80.Fn lgamma x ,
81.Fn lgammaf x ,
|
75and
| 82and
|
76.Fn lgammaf x
| 83.Fn lgammal 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
| 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
|
90.Fn lgamma_r x signgamp
| 97.Fn lgamma_r x signgamp ,
98.Fn lgammaf_r x signgamp ,
|
91and
| 99and
|
92.Fn lgammaf_r x signgamp
| 100.Fn lgammal_r x signgamp
|
93provide the same functionality as
| 101provide the same functionality as
|
94.Fn lgamma x
| 102.Fn lgamma x ,
103.Fn lgammaf x ,
|
95and
| 104and
|
96.Fn lgammaf x
| 105.Fn lgammal 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 .
105.Pp
106.Fn gamma ,
107.Fn gammaf ,
108.Fn gamma_r ,
109and
110.Fn gammaf_r
111are deprecated aliases for
112.Fn lgamma ,
113.Fn lgammaf ,
114.Fn lgamma_r ,
115and
116.Fn lgammaf_r ,
117respectively.
| 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 .
114.Pp
115.Fn gamma ,
116.Fn gammaf ,
117.Fn gamma_r ,
118and
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
|
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
126.Pp
127Only after
128.Fn lgamma
129or
130.Fn lgammaf
131has returned can signgam be correct.
132.Pp
133For arguments in its range,
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 ,
| 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
136.Pp
137Only after
138.Fn lgamma
139or
140.Fn lgammaf
141has returned can signgam be correct.
142.Pp
143For arguments in its range,
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 ,
|
142.Fn gamma_r ,
| |
143.Fn gammaf ,
| 152.Fn gammaf ,
|
| 153.Fn gammal ,
154.Fn gamma_r ,
|
144.Fn gammaf_r ,
| 155.Fn gammaf_r ,
|
| 156.Fn gammal_r ,
|
145.Fn lgamma ,
| 157.Fn lgamma ,
|
146.Fn lgamma_r ,
| |
147.Fn lgammaf ,
| 158.Fn lgammaf ,
|
| 159.Fn lgammal ,
160.Fn lgamma_r ,
161.Fn lgammaf_r ,
|
148and
| 162and
|
149.Fn lgammaf_r
| 163.Fn lgammal_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 ,
| 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 ,
|
162.Fn tgamma ,
163and
164.Fn tgammaf
165functions are expected to conform to
166.St -isoC-99 .
167.Sh HISTORY
168The
169.Fn lgamma
170function appeared in
171.Bx 4.3 .
172The
173.Fn gamma
174function appeared in
175.Bx 4.4
176as a function which computed \(*G(x).
177This version was used in
178.Fx 1.1 .
179The name
180.Fn gamma
181was originally dedicated to the
182.Fn lgamma
183function,
184and that usage was restored by switching to Sun's fdlibm in
185.Fx 1.1.5 .
186The
187.Fn tgamma
188function appeared in
189.Fx 5.0 .
| 177.Fn tgamma ,
178and
179.Fn tgammaf
180functions are expected to conform to
181.St -isoC-99 .
182.Sh HISTORY
183The
184.Fn lgamma
185function appeared in
186.Bx 4.3 .
187The
188.Fn gamma
189function appeared in
190.Bx 4.4
191as a function which computed \(*G(x).
192This version was used in
193.Fx 1.1 .
194The name
195.Fn gamma
196was originally dedicated to the
197.Fn lgamma
198function,
199and that usage was restored by switching to Sun's fdlibm in
200.Fx 1.1.5 .
201The
202.Fn tgamma
203function appeared in
204.Fx 5.0 .
|