1.\" Copyright (c) 2017 Steven G. Kargl <kargl@FreeBSD.org> 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.\" 13.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 14.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 15.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 16.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 17.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 18.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 19.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 20.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 21.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 22.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 23.\" SUCH DAMAGE. 24.\" 25.\" $FreeBSD$ 26.\" 27.Dd June 6, 2018 28.Dt CLOG 3 29.Os 30.Sh NAME 31.Nm clog , 32.Nm clogf 33and 34.Nm clogl 35.Nd complex natural logarithm functions 36.Sh LIBRARY 37.Lb libm 38.Sh SYNOPSIS 39.In complex.h 40.Ft double complex 41.Fn clog "double complex z" 42.Ft float complex 43.Fn clogf "float complex z" 44.Ft long double complex 45.Fn clogl "long double complex z" 46.Sh DESCRIPTION 47The 48.Fn clog , 49.Fn clogf , 50and 51.Fn clogl 52functions compute the complex natural logarithm of 53.Fa z . 54with a branch cut along the negative real axis . 55.Sh RETURN VALUES 56The 57.Fn clog 58function returns the complex natural logarithm value, in the 59range of a strip mathematically unbounded along the real axis and in 60the interval [-I* \*(Pi , +I* \*(Pi ] along the imaginary axis. 61The function satisfies the relationship: 62.Fo clog 63.Fn conj "z" Fc 64= 65.Fo conj 66.Fn clog "z" Fc . 67.Pp 68.\" Table is formatted for an 80-column xterm. 69.Bl -column ".Sy +\*(If + I*\*(Na" ".Sy Return value" ".Sy Divide-by-zero exception" 70.It Sy Argument Ta Sy Return value Ta Sy Comment 71.It -0 + I*0 Ta -\*(If + I*\*(Pi Ta Divide-by-zero exception 72.It Ta Ta raised 73.It +0 + I*0 Ta -\*(If + I*0 Ta Divide by zero exception 74.It Ta Ta raised 75.It x + I*\*(If Ta +\*(If + I*\*(Pi/2 Ta For finite x 76.It x + I*\*(Na Ta \*(Na + I*\*(Na Ta Optionally raises invalid 77.It Ta Ta floating-point exception 78.It Ta Ta for finite x 79.It -\*(If + I*y Ta +\*(If + I*\*(Pi Ta For finite positive-signed y 80.It +\*(If + I*y Ta +\*(If + I*0 Ta For finite positive-signed y 81.It -\*(If + I*\*(If Ta +\*(If + I*3\*(Pi/4 82.It +\*(If + I*\*(If Ta +\*(If + I*\*(Pi/4 83.It \*(Pm\*(If + I*\*(Na Ta +\*(If + I*\*(Na 84.It \*(Na + I*y Ta \*(Na + I*\*(Na Ta Optionally raises invalid 85.It Ta Ta floating-point exception 86.It Ta Ta for finite y 87.It \*(Na + I*\*(If Ta +\*(If + I*\*(Na 88.It \*(Na + I*\*(Na Ta \*(Na + I*\*(Na 89.El 90.Sh SEE ALSO 91.Xr complex 3 , 92.Xr log 3 , 93.Xr math 3 94.Sh STANDARDS 95The 96.Fn clog , 97.Fn cexpf , 98and 99.Fn clogl 100functions conform to 101.St -isoC-99 . 102