1.\" $OpenBSD: catan.3,v 1.2 2013/06/05 03:40:26 tedu Exp $ 2.\" 3.\" Copyright (c) 2011 Martynas Venckus <martynas@openbsd.org> 4.\" 5.\" Permission to use, copy, modify, and distribute this software for any 6.\" purpose with or without fee is hereby granted, provided that the above 7.\" copyright notice and this permission notice appear in all copies. 8.\" 9.\" THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES 10.\" WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF 11.\" MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR 12.\" ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 13.\" WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN 14.\" ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF 15.\" OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 16.\" 17.Dd $Mdocdate: June 5 2013 $ 18.Dt CATAN 3 19.Os 20.Sh NAME 21.Nm catan , 22.Nm catanf , 23.Nm catanl 24.Nd complex circular arc tangent 25.Sh SYNOPSIS 26.In complex.h 27.Ft double complex 28.Fn catan "double complex z" 29.Ft float complex 30.Fn catanf "float complex z" 31.Ft long double complex 32.Fn catanl "long double complex z" 33.Sh DESCRIPTION 34The 35.Fn catan , 36.Fn catanf 37and 38.Fn catanl 39functions compute the complex circular arc tangent of 40.Fa z . 41.Pp 42If 43.Fa z 44= x + iy, then 45.Bd -literal -offset indent 46Re catan(z) = 1/2 * atan(2x / (1 - x^2 - y^2)) + k Pi. 47Im catan(z) = 1/4 * log((x^2 + (y + 1)^2) / (x^2 + (y - 1)^2)). 48.Ed 49.Sh RETURN VALUES 50The 51.Fn catan , 52.Fn catanf 53and 54.Fn catanl 55functions return the complex circular arc tangent of 56.Fa z 57with unbounded imaginary part, and real part in the interval 58.Bq -Pi/2, Pi/2 . 59.Sh SEE ALSO 60.Xr cacos 3 , 61.Xr casin 3 62.Sh STANDARDS 63The 64.Fn catan , 65.Fn catanf 66and 67.Fn catanl 68functions conform to 69.St -isoC-99 . 70