xref: /freebsd/lib/msun/man/clog.3 (revision fa9896e082a1046ff4fbc75fcba4d18d1f2efc19)

.\" Copyright (c) 2017 Steven G. Kargl <kargl@FreeBSD.org>
.\" All rights reserved.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions
.\" are met:
.\" 1. Redistributions of source code must retain the above copyright
.\"    notice, this list of conditions and the following disclaimer.
.\" 2. Redistributions in binary form must reproduce the above copyright
.\"    notice, this list of conditions and the following disclaimer in the
.\"    documentation and/or other materials provided with the distribution.
.\"
.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
.\" SUCH DAMAGE.
.\"
.Dd June 6, 2018
.Dt CLOG 3
.Os
.Sh NAME
.Nm clog ,
.Nm clogf
and
.Nm clogl
.Nd complex natural logarithm functions
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In complex.h
.Ft double complex
.Fn clog "double complex z"
.Ft float complex
.Fn clogf "float complex z"
.Ft long double complex
.Fn clogl "long double complex z"
.Sh DESCRIPTION
The
.Fn clog ,
.Fn clogf ,
and
.Fn clogl
functions compute the complex natural logarithm of
.Fa z .
with a branch cut along the negative real axis .
.Sh RETURN VALUES
The
.Fn clog
function returns the complex natural logarithm value, in the
range of a strip mathematically unbounded along the real axis and in
the interval [-I* \*(Pi , +I* \*(Pi ] along the imaginary axis.
The function satisfies the relationship:
.Fo clog
.Fn conj "z" Fc
=
.Fo conj
.Fn clog "z" Fc .
.Pp
.\" Table is formatted for an 80-column xterm.
.Bl -column ".Sy +\*(If + I*\*(Na" ".Sy Return value" ".Sy Divide-by-zero exception"
.It Sy Argument          Ta Sy Return value Ta Sy Comment
.It -0 + I*0             Ta -\*(If + I*\*(Pi    Ta Divide-by-zero exception
.It                      Ta                     Ta raised
.It +0 + I*0             Ta -\*(If + I*0        Ta Divide by zero exception
.It                      Ta                     Ta raised
.It x + I*\*(If          Ta +\*(If + I*\*(Pi/2  Ta For finite x
.It x + I*\*(Na          Ta  \*(Na + I*\*(Na    Ta Optionally raises invalid
.It                      Ta                     Ta floating-point exception
.It                      Ta                     Ta for finite x
.It -\*(If + I*y         Ta +\*(If + I*\*(Pi    Ta For finite positive-signed y
.It +\*(If + I*y         Ta +\*(If + I*0        Ta For finite positive-signed y
.It -\*(If + I*\*(If     Ta +\*(If + I*3\*(Pi/4
.It +\*(If + I*\*(If     Ta +\*(If + I*\*(Pi/4
.It \*(Pm\*(If + I*\*(Na Ta +\*(If + I*\*(Na
.It \*(Na + I*y          Ta \*(Na + I*\*(Na    Ta Optionally raises invalid
.It                      Ta                    Ta floating-point exception
.It                      Ta                    Ta for finite y
.It \*(Na + I*\*(If      Ta +\*(If + I*\*(Na
.It \*(Na + I*\*(Na      Ta \*(Na + I*\*(Na
.El
.Sh SEE ALSO
.Xr complex 3 ,
.Xr log 3 ,
.Xr math 3
.Sh STANDARDS
The
.Fn clog ,
.Fn cexpf ,
and
.Fn clogl
functions conform to
.St -isoC-99 .