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