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.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 .