| lgamma.3 (176388) | lgamma.3 (271651) |
|---|---|
| 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 | 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 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 , |
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| 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 --- 6 unchanged lines hidden (view full) --- 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 --- 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" |
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| 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 . --- 5 unchanged lines hidden (view full) --- 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 . --- 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 |
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| 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 --- 8 unchanged lines hidden (view full) --- 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 --- 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 , |
| 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 , |
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| 162.Fn tgamma , 163and 164.Fn tgammaf 165functions are expected to conform to 166.St -isoC-99 . 167.Sh HISTORY 168The 169.Fn lgamma --- 20 unchanged lines hidden --- | 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 --- |