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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.Dd December 8, 2017 29.Dt LGAMMA 3 30.Os 31.Sh NAME 32.Nm lgamma , 33.Nm lgamma_r , 34.Nm lgammaf , 35.Nm lgammaf_r , 36.Nm lgammal , 37.Nm lgammal_r , 38.Nm gamma , 39.Nm gamma_r , 40.Nm gammaf , 41.Nm gammaf_r , 42.Nm tgamma , 43.Nm tgammaf , 44.Nm tgammal , 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" 61.Ft "long double" 62.Fn lgammal "long double x" 63.Ft "long double" 64.Fn lgammal_r "long double x" "int *signgamp" 65.Ft double 66.Fn gamma "double x" 67.Ft double 68.Fn gamma_r "double x" "int *signgamp" 69.Ft float 70.Fn gammaf "float x" 71.Ft float 72.Fn gammaf_r "float x" "int *signgamp" 73.Ft "long double" 74.Fn tgamma "double x" 75.Ft float 76.Fn tgammaf "float x" 77.Ft "long double" 78.Fn tgammal "long double 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 , 110.Fn tgammaf x , 111and 112.Fn tgammal x 113functions return \(*G(x), with no effect on 114.Fa signgam . 115.Pp 116.Fn gamma , 117.Fn gammaf , 118.Fn gamma_r , 119and 120.Fn gammaf_r 121are deprecated aliases for 122.Fn lgamma , 123.Fn lgammaf , 124.Fn lgamma_r , 125and 126.Fn lgammaf_r , 127respectively. 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 , 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 BUGS 171To conform with newer C/C++ standards, a stub implementation for 172.Nm tgammal 173was committed to the math library, where 174.Nm tgammal 175is mapped to 176.Nm tgamma . 177Thus, the numerical accuracy is at most that of the 53-bit double 178precision implementation. 179.Sh SEE ALSO 180.Xr math 3 181.Sh STANDARDS 182The 183.Fn lgamma , 184.Fn lgammaf , 185.Fn lgammal , 186.Fn tgamma , 187.Fn tgammaf , 188and 189.Fn tgammal 190functions are expected to conform to 191.St -isoC-99 . 192.Sh HISTORY 193The 194.Fn lgamma 195function appeared in 196.Bx 4.3 . 197The 198.Fn gamma 199function appeared in 200.Bx 4.4 201as a function which computed \(*G(x). 202This version was used in 203.Fx 1.1 . 204The name 205.Fn gamma 206was originally dedicated to the 207.Fn lgamma 208function, 209and that usage was restored by switching to Sun's fdlibm in 210.Fx 1.1.5 . 211The 212.Fn tgamma 213function appeared in 214.Fx 5.0 . 215