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.\" $NetBSD: atan2.3,v 1.14 2002/10/01 19:21:30 wiz Exp $ 34.\" 35.Dd May 2, 1991 36.Dt ATAN2 3 37.Os 38.Sh NAME 39.Nm atan2 , 40.Nm atan2f 41.Nd arc tangent function of two variables 42.Sh LIBRARY 43.Lb libm 44.Sh SYNOPSIS 45.Fd #include \*[Lt]math.h\*[Gt] 46.Ft double 47.Fn atan2 "double y" "double x" 48.Ft float 49.Fn atan2f "float y" "float x" 50.Sh DESCRIPTION 51The 52.Fn atan2 53and 54.Fn atan2f 55functions compute the principal value of the arc tangent of 56.Ar y/ Ns Ar x , 57using the signs of both arguments to determine the quadrant of 58the return value. 59.Sh RETURN VALUES 60The 61.Fn atan2 62function, if successful, 63returns the arc tangent of 64.Ar y/ Ns Ar x 65in the range 66.Bk -words 67.Bq \&- Ns \*(Pi , \&+ Ns \*(Pi 68.Ek 69radians. 70If both 71.Ar x 72and 73.Ar y 74are zero, the global variable 75.Va errno 76is set to 77.Er EDOM . 78On the 79.Tn VAX : 80.Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___ 81.It Fn atan2 y x No := Ta 82.Fn atan y/x Ta 83if 84.Ar x 85\*[Gt] 0, 86.It Ta sign( Ns Ar y Ns )*(\*(Pi - 87.Fn atan "\\*(Bay/x\\*(Ba" ) Ta 88if 89.Ar x 90\*[Lt] 0, 91.It Ta 92.No 0 Ta 93if x = y = 0, or 94.It Ta 95.Pf sign( Ar y Ns )*\\*(Pi/2 Ta 96if 97.Ar x 98= 0 \*(!= 99.Ar y . 100.El 101.Sh NOTES 102The function 103.Fn atan2 104defines "if x \*[Gt] 0," 105.Fn atan2 0 0 106= 0 on a 107.Tn VAX 108despite that previously 109.Fn atan2 0 0 110may have generated an error message. 111The reasons for assigning a value to 112.Fn atan2 0 0 113are these: 114.Bl -enum -offset indent 115.It 116Programs that test arguments to avoid computing 117.Fn atan2 0 0 118must be indifferent to its value. 119Programs that require it to be invalid are vulnerable 120to diverse reactions to that invalidity on diverse computer systems. 121.It 122The 123.Fn atan2 124function is used mostly to convert from rectangular (x,y) 125to polar 126.if n\ 127(r,theta) 128.if t\ 129(r,\(*h) 130coordinates that must satisfy x = 131.if n\ 132r\(**cos theta 133.if t\ 134r\(**cos\(*h 135and y = 136.if n\ 137r\(**sin theta. 138.if t\ 139r\(**sin\(*h. 140These equations are satisfied when (x=0,y=0) 141is mapped to 142.if n \ 143(r=0,theta=0) 144.if t \ 145(r=0,\(*h=0) 146on a VAX. 147In general, conversions to polar coordinates should be computed thus: 148.Bd -unfilled -offset indent 149.if n \{\ 150r := hypot(x,y); ... := sqrt(x\(**x+y\(**y) 151theta := atan2(y,x). 152.\} 153.if t \{\ 154r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d) 155\(*h := atan2(y,x). 156.\} 157.Ed 158.It 159The foregoing formulas need not be altered to cope in a 160reasonable way with signed zeros and infinities 161on a machine that conforms to 162.Tn IEEE 754 ; 163the versions of 164.Xr hypot 3 165and 166.Fn atan2 167provided for 168such a machine are designed to handle all cases. 169That is why 170.Fn atan2 \(+-0 \-0 171= \(+-\*(Pi 172for instance. 173In general the formulas above are equivalent to these: 174.Bd -unfilled -offset indent 175.if n \ 176r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x); 177.if t \ 178r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x); 179.Ed 180.El 181.Sh SEE ALSO 182.Xr acos 3 , 183.Xr asin 3 , 184.Xr atan 3 , 185.Xr cos 3 , 186.Xr cosh 3 , 187.Xr math 3 , 188.Xr sin 3 , 189.Xr sinh 3 , 190.Xr tan 3 , 191.Xr tanh 3 192.Sh STANDARDS 193The 194.Fn atan2 195function conforms to 196.St -ansiC . 197