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.Dd June 6, 2018 26.Dt CLOG 3 27.Os 28.Sh NAME 29.Nm clog , 30.Nm clogf 31and 32.Nm clogl 33.Nd complex natural logarithm functions 34.Sh LIBRARY 35.Lb libm 36.Sh SYNOPSIS 37.In complex.h 38.Ft double complex 39.Fn clog "double complex z" 40.Ft float complex 41.Fn clogf "float complex z" 42.Ft long double complex 43.Fn clogl "long double complex z" 44.Sh DESCRIPTION 45The 46.Fn clog , 47.Fn clogf , 48and 49.Fn clogl 50functions compute the complex natural logarithm of 51.Fa z . 52with a branch cut along the negative real axis . 53.Sh RETURN VALUES 54The 55.Fn clog 56function returns the complex natural logarithm value, in the 57range of a strip mathematically unbounded along the real axis and in 58the interval [-I* \*(Pi , +I* \*(Pi ] along the imaginary axis. 59The function satisfies the relationship: 60.Fo clog 61.Fn conj "z" Fc 62= 63.Fo conj 64.Fn clog "z" Fc . 65.Pp 66.\" Table is formatted for an 80-column xterm. 67.Bl -column ".Sy +\*(If + I*\*(Na" ".Sy Return value" ".Sy Divide-by-zero exception" 68.It Sy Argument Ta Sy Return value Ta Sy Comment 69.It -0 + I*0 Ta -\*(If + I*\*(Pi Ta Divide-by-zero exception 70.It Ta Ta raised 71.It +0 + I*0 Ta -\*(If + I*0 Ta Divide by zero exception 72.It Ta Ta raised 73.It x + I*\*(If Ta +\*(If + I*\*(Pi/2 Ta For finite x 74.It x + I*\*(Na Ta \*(Na + I*\*(Na Ta Optionally raises invalid 75.It Ta Ta floating-point exception 76.It Ta Ta for finite x 77.It -\*(If + I*y Ta +\*(If + I*\*(Pi Ta For finite positive-signed y 78.It +\*(If + I*y Ta +\*(If + I*0 Ta For finite positive-signed y 79.It -\*(If + I*\*(If Ta +\*(If + I*3\*(Pi/4 80.It +\*(If + I*\*(If Ta +\*(If + I*\*(Pi/4 81.It \*(Pm\*(If + I*\*(Na Ta +\*(If + I*\*(Na 82.It \*(Na + I*y Ta \*(Na + I*\*(Na Ta Optionally raises invalid 83.It Ta Ta floating-point exception 84.It Ta Ta for finite y 85.It \*(Na + I*\*(If Ta +\*(If + I*\*(Na 86.It \*(Na + I*\*(Na Ta \*(Na + I*\*(Na 87.El 88.Sh SEE ALSO 89.Xr complex 3 , 90.Xr log 3 , 91.Xr math 3 92.Sh STANDARDS 93The 94.Fn clog , 95.Fn cexpf , 96and 97.Fn clogl 98functions conform to 99.St -isoC-99 . 100