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 --- 6 unchanged lines hidden (view full) --- 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 . --- 5 unchanged lines hidden (view full) --- 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 --- 8 unchanged lines hidden (view full) --- 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 --- 20 unchanged lines hidden --- |