1.\" Copyright (c) 1991 The Regents of the University of California. 2.\" All rights reserved. 3.\" 4.\" Redistribution and use in source and binary forms, with or without 5.\" modification, are permitted provided that the following conditions 6.\" are met: 7.\" 1. Redistributions of source code must retain the above copyright 8.\" notice, this list of conditions and the following disclaimer. 9.\" 2. Redistributions in binary form must reproduce the above copyright 10.\" notice, this list of conditions and the following disclaimer in the 11.\" documentation and/or other materials provided with the distribution. 12.\" 3. All advertising materials mentioning features or use of this software 13.\" must display the following acknowledgement: 14.\" This product includes software developed by the University of 15.\" California, Berkeley and its contributors. 16.\" 4. Neither the name of the University nor the names of its contributors 17.\" may be used to endorse or promote products derived from this software 18.\" without specific prior written permission. 19.\" 20.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 21.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 22.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 23.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 24.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 25.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 26.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 27.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 28.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 29.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 30.\" SUCH DAMAGE. 31.\" 32.\" from: @(#)atan2.3 5.1 (Berkeley) 5/2/91 33.\" $Id: atan2.3,v 1.3 1993/08/14 13:42:32 mycroft Exp $ 34.\" 35.Dd May 2, 1991 36.Dt ATAN2 3 37.Os 38.Sh NAME 39.Nm atan2 40.Nd arc tangent function of two variables 41.Sh SYNOPSIS 42.Fd #include <math.h> 43.Ft double 44.Fn atan2 "double y" "double x" 45.Sh DESCRIPTION 46The 47.Xr atan2 48function computes the principal value of the arc tangent of 49.Ar y/ Ns Ar x , 50using the signs of both arguments to determine the quadrant of 51the return value. 52.Sh RETURN VALUES 53The 54.Xr atan2 55function, if successful, 56returns the arc tangent of 57.Ar y/ Ns Ar x 58in the range 59.Bk -words 60.Bq \&- Ns \*(Pi , \&+ Ns \*(Pi 61.Ek 62radians. 63If both 64.Ar x 65and 66.Ar y 67are zero, the global variable 68.Va errno 69is set to 70.Er EDOM . 71On the 72.Tn VAX : 73.Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___ 74.It Fn atan2 y x No := Ta 75.Fn atan y/x Ta 76if 77.Ar x 78> 0, 79.It Ta sign( Ns Ar y Ns )*(\*(Pi - 80.Fn atan "\\*(Bay/x\\*(Ba" ) Ta 81if 82.Ar x 83< 0, 84.It Ta 85.No 0 Ta 86if x = y = 0, or 87.It Ta 88.Pf sign( Ar y Ns )*\\*(Pi/2 Ta 89if 90.Ar x 91= 0 \*(!= 92.Ar y . 93.El 94.Sh NOTES 95The function 96.Fn atan2 97defines "if x > 0," 98.Fn atan2 0 0 99= 0 on a 100.Tn VAX 101despite that previously 102.Fn atan2 0 0 103may have generated an error message. 104The reasons for assigning a value to 105.Fn atan2 0 0 106are these: 107.Bl -enum -offset indent 108.It 109Programs that test arguments to avoid computing 110.Fn atan2 0 0 111must be indifferent to its value. 112Programs that require it to be invalid are vulnerable 113to diverse reactions to that invalidity on diverse computer systems. 114.It 115The 116.Fn atan2 117function is used mostly to convert from rectangular (x,y) 118to polar 119.if n\ 120(r,theta) 121.if t\ 122(r,\(*h) 123coordinates that must satisfy x = 124.if n\ 125r\(**cos theta 126.if t\ 127r\(**cos\(*h 128and y = 129.if n\ 130r\(**sin theta. 131.if t\ 132r\(**sin\(*h. 133These equations are satisfied when (x=0,y=0) 134is mapped to 135.if n \ 136(r=0,theta=0) 137.if t \ 138(r=0,\(*h=0) 139on a VAX. In general, conversions to polar coordinates 140should be computed thus: 141.Bd -unfilled -offset indent 142.if n \{\ 143r := hypot(x,y); ... := sqrt(x\(**x+y\(**y) 144theta := atan2(y,x). 145.\} 146.if t \{\ 147r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d) 148\(*h := atan2(y,x). 149.\} 150.Ed 151.It 152The foregoing formulas need not be altered to cope in a 153reasonable way with signed zeros and infinities 154on a machine that conforms to 155.Tn IEEE 754 ; 156the versions of 157.Xr hypot 3 158and 159.Fn atan2 160provided for 161such a machine are designed to handle all cases. 162That is why 163.Fn atan2 \(+-0 \-0 164= \(+-\*(Pi 165for instance. 166In general the formulas above are equivalent to these: 167.Bd -unfilled -offset indent 168.if n \ 169r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x); 170.if t \ 171r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x); 172.Ed 173.El 174.Sh SEE ALSO 175.Xr acos 3 , 176.Xr asin 3 , 177.Xr atan 3 , 178.Xr cos 3 , 179.Xr cosh 3 , 180.Xr sin 3 , 181.Xr sinh 3 , 182.Xr tan 3 , 183.Xr tanh 3 , 184.Xr math 3 , 185.Sh STANDARDS 186The 187.Fn atan2 188function conforms to 189.St -ansiC . 190