1*05a0b428SJohn Marino.\" $OpenBSD: catan.3,v 1.2 2013/06/05 03:40:26 tedu Exp $ 2*05a0b428SJohn Marino.\" 3*05a0b428SJohn Marino.\" Copyright (c) 2011 Martynas Venckus <martynas@openbsd.org> 4*05a0b428SJohn Marino.\" 5*05a0b428SJohn Marino.\" Permission to use, copy, modify, and distribute this software for any 6*05a0b428SJohn Marino.\" purpose with or without fee is hereby granted, provided that the above 7*05a0b428SJohn Marino.\" copyright notice and this permission notice appear in all copies. 8*05a0b428SJohn Marino.\" 9*05a0b428SJohn Marino.\" THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES 10*05a0b428SJohn Marino.\" WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF 11*05a0b428SJohn Marino.\" MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR 12*05a0b428SJohn Marino.\" ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 13*05a0b428SJohn Marino.\" WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN 14*05a0b428SJohn Marino.\" ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF 15*05a0b428SJohn Marino.\" OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 16*05a0b428SJohn Marino.\" 17*05a0b428SJohn Marino.Dd $Mdocdate: June 5 2013 $ 18*05a0b428SJohn Marino.Dt CATAN 3 19*05a0b428SJohn Marino.Os 20*05a0b428SJohn Marino.Sh NAME 21*05a0b428SJohn Marino.Nm catan , 22*05a0b428SJohn Marino.Nm catanf , 23*05a0b428SJohn Marino.Nm catanl 24*05a0b428SJohn Marino.Nd complex circular arc tangent 25*05a0b428SJohn Marino.Sh SYNOPSIS 26*05a0b428SJohn Marino.In complex.h 27*05a0b428SJohn Marino.Ft double complex 28*05a0b428SJohn Marino.Fn catan "double complex z" 29*05a0b428SJohn Marino.Ft float complex 30*05a0b428SJohn Marino.Fn catanf "float complex z" 31*05a0b428SJohn Marino.Ft long double complex 32*05a0b428SJohn Marino.Fn catanl "long double complex z" 33*05a0b428SJohn Marino.Sh DESCRIPTION 34*05a0b428SJohn MarinoThe 35*05a0b428SJohn Marino.Fn catan , 36*05a0b428SJohn Marino.Fn catanf 37*05a0b428SJohn Marinoand 38*05a0b428SJohn Marino.Fn catanl 39*05a0b428SJohn Marinofunctions compute the complex circular arc tangent of 40*05a0b428SJohn Marino.Fa z . 41*05a0b428SJohn Marino.Pp 42*05a0b428SJohn MarinoIf 43*05a0b428SJohn Marino.Fa z 44*05a0b428SJohn Marino= x + iy, then 45*05a0b428SJohn Marino.Bd -literal -offset indent 46*05a0b428SJohn MarinoRe catan(z) = 1/2 * atan(2x / (1 - x^2 - y^2)) + k Pi. 47*05a0b428SJohn MarinoIm catan(z) = 1/4 * log((x^2 + (y + 1)^2) / (x^2 + (y - 1)^2)). 48*05a0b428SJohn Marino.Ed 49*05a0b428SJohn Marino.Sh RETURN VALUES 50*05a0b428SJohn MarinoThe 51*05a0b428SJohn Marino.Fn catan , 52*05a0b428SJohn Marino.Fn catanf 53*05a0b428SJohn Marinoand 54*05a0b428SJohn Marino.Fn catanl 55*05a0b428SJohn Marinofunctions return the complex circular arc tangent of 56*05a0b428SJohn Marino.Fa z 57*05a0b428SJohn Marinowith unbounded imaginary part, and real part in the interval 58*05a0b428SJohn Marino.Bq -Pi/2, Pi/2 . 59*05a0b428SJohn Marino.Sh SEE ALSO 60*05a0b428SJohn Marino.Xr cacos 3 , 61*05a0b428SJohn Marino.Xr casin 3 62*05a0b428SJohn Marino.Sh STANDARDS 63*05a0b428SJohn MarinoThe 64*05a0b428SJohn Marino.Fn catan , 65*05a0b428SJohn Marino.Fn catanf 66*05a0b428SJohn Marinoand 67*05a0b428SJohn Marino.Fn catanl 68*05a0b428SJohn Marinofunctions conform to 69*05a0b428SJohn Marino.St -isoC-99 . 70