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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.\" $FreeBSD$ 30.\" 31.Dd December 8, 2017 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.Nm tgammal , 48.Nd log gamma functions, gamma function 49.Sh LIBRARY 50.Lb libm 51.Sh SYNOPSIS 52.In math.h 53.Ft extern int 54.Fa signgam ; 55.sp 56.Ft double 57.Fn lgamma "double x" 58.Ft double 59.Fn lgamma_r "double x" "int *signgamp" 60.Ft float 61.Fn lgammaf "float x" 62.Ft float 63.Fn lgammaf_r "float x" "int *signgamp" 64.Ft "long double" 65.Fn lgammal "long double x" 66.Ft "long double" 67.Fn lgammal_r "long double x" "int *signgamp" 68.Ft double 69.Fn gamma "double x" 70.Ft double 71.Fn gamma_r "double x" "int *signgamp" 72.Ft float 73.Fn gammaf "float x" 74.Ft float 75.Fn gammaf_r "float x" "int *signgamp" 76.Ft "long double" 77.Fn tgamma "double x" 78.Ft float 79.Fn tgammaf "float x" 80.Ft "long double" 81.Fn tgammal "long double x" 82.Sh DESCRIPTION 83.Fn lgamma x , 84.Fn lgammaf x , 85and 86.Fn lgammal x 87.if t \{\ 88return ln\||\(*G(x)| where 89.Bd -unfilled -offset indent 90\(*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 91\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1. 92.Ed 93.\} 94.if n \ 95return ln\||\(*G(x)|. 96The external integer 97.Fa signgam 98returns the sign of \(*G(x). 99.Pp 100.Fn lgamma_r x signgamp , 101.Fn lgammaf_r x signgamp , 102and 103.Fn lgammal_r x signgamp 104provide the same functionality as 105.Fn lgamma x , 106.Fn lgammaf x , 107and 108.Fn lgammal x , 109but the caller must provide an integer to store the sign of \(*G(x). 110.Pp 111The 112.Fn tgamma x , 113.Fn tgammaf x , 114and 115.Fn tgammal x 116functions return \(*G(x), with no effect on 117.Fa signgam . 118.Pp 119.Fn gamma , 120.Fn gammaf , 121.Fn gamma_r , 122and 123.Fn gammaf_r 124are deprecated aliases for 125.Fn lgamma , 126.Fn lgammaf , 127.Fn lgamma_r , 128and 129.Fn lgammaf_r , 130respectively. 131.Sh IDIOSYNCRASIES 132Do not use the expression 133.Dq Li signgam\(**exp(lgamma(x)) 134to compute g := \(*G(x). 135Instead use a program like this (in C): 136.Bd -literal -offset indent 137lg = lgamma(x); g = signgam\(**exp(lg); 138.Ed 139.Pp 140Only after 141.Fn lgamma 142or 143.Fn lgammaf 144has returned can signgam be correct. 145.Pp 146For arguments in its range, 147.Fn tgamma 148is preferred, as for positive arguments 149it is accurate to within one unit in the last place. 150Exponentiation of 151.Fn lgamma 152will lose up to 10 significant bits. 153.Sh RETURN VALUES 154.Fn gamma , 155.Fn gammaf , 156.Fn gammal , 157.Fn gamma_r , 158.Fn gammaf_r , 159.Fn gammal_r , 160.Fn lgamma , 161.Fn lgammaf , 162.Fn lgammal , 163.Fn lgamma_r , 164.Fn lgammaf_r , 165and 166.Fn lgammal_r 167return appropriate values unless an argument is out of range. 168Overflow will occur for sufficiently large positive values, and 169non-positive integers. 170For large non-integer negative values, 171.Fn tgamma 172will underflow. 173.Sh BUGS 174To conform with newer C/C++ standards, a stub implementation for 175.Nm tgammal 176was committed to the math library, where 177.Nm tgammal 178is mapped to 179.Nm tgamma . 180Thus, the numerical accuracy is at most that of the 53-bit double 181precision implementation. 182.Sh SEE ALSO 183.Xr math 3 184.Sh STANDARDS 185The 186.Fn lgamma , 187.Fn lgammaf , 188.Fn lgammal , 189.Fn tgamma , 190.Fn tgammaf , 191and 192.Fn tgammal 193functions are expected to conform to 194.St -isoC-99 . 195.Sh HISTORY 196The 197.Fn lgamma 198function appeared in 199.Bx 4.3 . 200The 201.Fn gamma 202function appeared in 203.Bx 4.4 204as a function which computed \(*G(x). 205This version was used in 206.Fx 1.1 . 207The name 208.Fn gamma 209was originally dedicated to the 210.Fn lgamma 211function, 212and that usage was restored by switching to Sun's fdlibm in 213.Fx 1.1.5 . 214The 215.Fn tgamma 216function appeared in 217.Fx 5.0 . 218