1.\" $OpenBSD: atan2.3,v 1.9 2003/06/02 20:18:41 millert Exp $ 2.\" Copyright (c) 1991 The Regents of the University of California. 3.\" All rights reserved. 4.\" 5.\" Redistribution and use in source and binary forms, with or without 6.\" modification, are permitted provided that the following conditions 7.\" are met: 8.\" 1. Redistributions of source code must retain the above copyright 9.\" notice, this list of conditions and the following disclaimer. 10.\" 2. Redistributions in binary form must reproduce the above copyright 11.\" notice, this list of conditions and the following disclaimer in the 12.\" documentation and/or other materials provided with the distribution. 13.\" 3. Neither the name of the University nor the names of its contributors 14.\" may be used to endorse or promote products derived from this software 15.\" without specific prior written permission. 16.\" 17.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 18.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 19.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 20.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 21.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 22.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 23.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 24.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 25.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 26.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 27.\" SUCH DAMAGE. 28.\" 29.\" from: @(#)atan2.3 5.1 (Berkeley) 5/2/91 30.\" 31.Dd May 2, 1991 32.Dt ATAN2 3 33.Os 34.Sh NAME 35.Nm atan2 , 36.Nm atan2f 37.Nd arc tangent functions of two variables 38.Sh SYNOPSIS 39.Fd #include <math.h> 40.Ft double 41.Fn atan2 "double y" "double x" 42.Ft float 43.Fn atan2f "float y" "float x" 44.Sh DESCRIPTION 45The 46.Fn atan2 47function computes the principal value of the arc tangent of 48.Ar y/ Ns Ar x , 49using the signs of both arguments to determine the quadrant of 50the return value. 51The 52.Fn atan2f 53function is a single precision version of 54.Fn atan2 . 55.Sh RETURN VALUES 56The 57.Fn atan2 58and 59.Fn atan2f 60functions, if successful, 61return the arc tangent of 62.Ar y/ Ns Ar x 63in the range 64.Bk -words 65.Bq \&- Ns \*(Pi , \&+ Ns \*(Pi 66.Ek 67radians. 68If both 69.Ar x 70and 71.Ar y 72are zero, the global variable 73.Va errno 74is set to 75.Er EDOM . 76On the 77.Tn VAX : 78.Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___ 79.It Fn atan2 y x No := Ta 80.Fn atan y/x Ta 81if 82.Ar x 83> 0, 84.It Ta sign( Ns Ar y Ns )*(\*(Pi - 85.Fn atan "\\*(Bay/x\\*(Ba" ) Ta 86if 87.Ar x 88< 0, 89.It Ta 90.No 0 Ta 91if x = y = 0, or 92.It Ta 93.Pf sign( Ar y Ns )*\\*(Pi/2 Ta 94if 95.Ar x 96= 0 \*(!= 97.Ar y . 98.El 99.Sh NOTES 100The function 101.Fn atan2 102defines "if x > 0," 103.Fn atan2 0 0 104= 0 on a 105.Tn VAX 106despite that previously 107.Fn atan2 0 0 108may have generated an error message. 109The reasons for assigning a value to 110.Fn atan2 0 0 111are these: 112.Bl -enum -offset indent 113.It 114Programs that test arguments to avoid computing 115.Fn atan2 0 0 116must be indifferent to its value. 117Programs that require it to be invalid are vulnerable 118to diverse reactions to that invalidity on diverse computer systems. 119.It 120The 121.Fn atan2 122function is used mostly to convert from rectangular (x,y) 123to polar 124.if n\ 125(r,theta) 126.if t\ 127(r,\(*h) 128coordinates that must satisfy x = 129.if n\ 130r\(**cos theta 131.if t\ 132r\(**cos\(*h 133and y = 134.if n\ 135r\(**sin theta. 136.if t\ 137r\(**sin\(*h. 138These equations are satisfied when (x=0,y=0) 139is mapped to 140.if n \ 141(r=0,theta=0) 142.if t \ 143(r=0,\(*h=0) 144on a VAX. In general, conversions to polar coordinates 145should be computed thus: 146.Bd -unfilled -offset indent 147.if n \{\ 148r := hypot(x,y); ... := sqrt(x\(**x+y\(**y) 149theta := atan2(y,x). 150.\} 151.if t \{\ 152r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d) 153\(*h := atan2(y,x). 154.\} 155.Ed 156.It 157The foregoing formulas need not be altered to cope in a 158reasonable way with signed zeros and infinities 159on a machine that conforms to 160.Tn IEEE 754 ; 161the versions of 162.Xr hypot 3 163and 164.Fn atan2 165provided for 166such a machine are designed to handle all cases. 167That is why 168.Fn atan2 \(+-0 \-0 169= \(+-\*(Pi 170for instance. 171In general the formulas above are equivalent to these: 172.Bd -unfilled -offset indent 173.if n \ 174r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x); 175.if t \ 176r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x); 177.Ed 178.El 179.Sh SEE ALSO 180.Xr acos 3 , 181.Xr asin 3 , 182.Xr atan 3 , 183.Xr cos 3 , 184.Xr cosh 3 , 185.Xr math 3 , 186.Xr sin 3 , 187.Xr sinh 3 , 188.Xr tan 3 , 189.Xr tanh 3 190.Sh STANDARDS 191The 192.Fn atan2 193function conforms to 194.St -ansiC . 195