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.\" $FreeBSD$ 34.\" 35.Dd January 14, 2005 36.Dt ATAN2 3 37.Os 38.Sh NAME 39.Nm atan2 , 40.Nm atan2f 41.Nd arc tangent functions of two variables 42.Sh LIBRARY 43.Lb libm 44.Sh SYNOPSIS 45.In math.h 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 the 54.Fn atan2f 55functions compute the principal value of the arc tangent of 56.Fa 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 62and the 63.Fn atan2f 64functions, if successful, 65return the arc tangent of 66.Fa y/ Ns Ar x 67in the range 68.Bk -words 69.Bq \&- Ns \*(Pi , \&+ Ns \*(Pi 70.Ek 71radians. 72Here are some of the special cases: 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 despite that previously 100.Fn atan2 0 0 101may have generated an error message. 102The reasons for assigning a value to 103.Fn atan2 0 0 104are these: 105.Bl -enum -offset indent 106.It 107Programs that test arguments to avoid computing 108.Fn atan2 0 0 109must be indifferent to its value. 110Programs that require it to be invalid are vulnerable 111to diverse reactions to that invalidity on diverse computer systems. 112.It 113The 114.Fn atan2 115function is used mostly to convert from rectangular (x,y) 116to polar 117.if n\ 118(r,theta) 119.if t\ 120(r,\(*h) 121coordinates that must satisfy x = 122.if n\ 123r\(**cos theta 124.if t\ 125r\(**cos\(*h 126and y = 127.if n\ 128r\(**sin theta. 129.if t\ 130r\(**sin\(*h. 131These equations are satisfied when (x=0,y=0) 132is mapped to 133.if n \ 134(r=0,theta=0). 135.if t \ 136(r=0,\(*h=0). 137In general, conversions to polar coordinates 138should be computed thus: 139.Bd -unfilled -offset indent 140.if n \{\ 141r := hypot(x,y); ... := sqrt(x\(**x+y\(**y) 142theta := atan2(y,x). 143.\} 144.if t \{\ 145r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d) 146\(*h := atan2(y,x). 147.\} 148.Ed 149.It 150The foregoing formulas need not be altered to cope in a 151reasonable way with signed zeros and infinities 152on a machine that conforms to 153.Tn IEEE 754 ; 154the versions of 155.Xr hypot 3 156and 157.Fn atan2 158provided for 159such a machine are designed to handle all cases. 160That is why 161.Fn atan2 \(+-0 \-0 162= \(+-\*(Pi 163for instance. 164In general the formulas above are equivalent to these: 165.Bd -unfilled -offset indent 166.if n \ 167r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x); 168.if t \ 169r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x); 170.Ed 171.El 172.Sh SEE ALSO 173.Xr acos 3 , 174.Xr asin 3 , 175.Xr atan 3 , 176.Xr cos 3 , 177.Xr cosh 3 , 178.Xr math 3 , 179.Xr sin 3 , 180.Xr sinh 3 , 181.Xr tan 3 , 182.Xr tanh 3 183.Sh STANDARDS 184The 185.Fn atan2 186function conforms to 187.St -isoC . 188