.\"	$OpenBSD: catan.3,v 1.1 2011/07/20 17:50:43 martynas Exp $
.\"
.\" Copyright (c) 2011 Martynas Venckus <martynas@openbsd.org>
.\"
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.Dd $Mdocdate: July 20 2011 $
.Dt CATAN 3
.Os
.Sh NAME
.Nm catan ,
.Nm catanf ,
.Nm catanl
.Nd complex circular arc tangent
.Sh SYNOPSIS
.Fd #include <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 .