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.\" $OpenBSD: catan.3,v 1.2 2013/06/05 03:40:26 tedu Exp $
.\"
.\" Copyright (c) 2011 Martynas Venckus <martynas@openbsd.org>
.\"
.\" Permission to use, copy, modify, and distribute this software for any
.\" purpose with or without fee is hereby granted, provided that the above
.\" copyright notice and this permission notice appear in all copies.
.\"
.\" THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
.\" WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
.\" MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
.\" ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
.\" WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
.\" ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
.\" OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
.\"
.Dd $Mdocdate: June 5 2013 $
.Dt CATAN 3
.Os
.Sh NAME
.Nm catan ,
.Nm catanf ,
.Nm catanl
.Nd complex circular arc tangent
.Sh SYNOPSIS
.In complex.h
.Ft double complex
.Fn catan "double complex z"
.Ft float complex
.Fn catanf "float complex z"
.Ft long double complex
.Fn catanl "long double complex z"
.Sh DESCRIPTION
The
.Fn catan ,
.Fn catanf
and
.Fn catanl
functions compute the complex circular arc tangent of
.Fa z .
.Pp
If
.Fa z
= x + iy, then
.Bd -literal -offset indent
Re catan(z) = 1/2 * atan(2x / (1 - x^2 - y^2)) + k Pi.
Im catan(z) = 1/4 * log((x^2 + (y + 1)^2) / (x^2 + (y - 1)^2)).
.Ed
.Sh RETURN VALUES
The
.Fn catan ,
.Fn catanf
and
.Fn catanl
functions return the complex circular arc tangent of
.Fa z
with unbounded imaginary part, and real part in the interval
.Bq -Pi/2, Pi/2 .
.Sh SEE ALSO
.Xr cacos 3 ,
.Xr casin 3
.Sh STANDARDS
The
.Fn catan ,
.Fn catanf
and
.Fn catanl
functions conform to
.St -isoC-99 .
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