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.\" 4. Neither the name of the University nor the names of its contributors 13.\" may be used to endorse or promote products derived from this software 14.\" without specific prior written permission. 15.\" 16.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 17.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 18.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 19.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 20.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 21.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 22.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 23.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 24.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 25.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 26.\" SUCH DAMAGE. 27.\" 28.\" from: @(#)atan2.3 5.1 (Berkeley) 5/2/91 29.\" $FreeBSD$ 30.\" 31.Dd July 31, 2008 32.Dt ATAN2 3 33.Os 34.Sh NAME 35.Nm atan2 , 36.Nm atan2f , 37.Nm atan2l , 38.Nm carg , 39.Nm cargf , 40.Nm cargl 41.Nd arc tangent and complex phase angle functions 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.Ft long double 51.Fn atan2l "long double y" "long double x" 52.In complex.h 53.Ft double 54.Fn carg "double complex z" 55.Ft float 56.Fn cargf "float complex z" 57.Ft long double 58.Fn cargl "long double complex z" 59.Sh DESCRIPTION 60The 61.Fn atan2 , 62.Fn atan2f , 63and 64.Fn atan2l 65functions compute the principal value of the arc tangent of 66.Fa y/ Ns Ar x , 67using the signs of both arguments to determine the quadrant of 68the return value. 69.ie '\*[.T]'utf8' \{\ 70. ds Th \[*h] 71.\} 72.el \{\ 73. ds Th theta 74.\} 75.Pp 76The 77.Fn carg , 78.Fn cargf , 79and 80.Fn cargl 81functions compute the complex argument (or phase angle) of 82.Fa z . 83The complex argument is the number \*(Th such that 84.Li z = r * e^(I * \*(Th) , 85where 86.Li r = cabs(z) . 87The call 88.Li carg(z) 89is equivalent to 90.Li atan2(cimag(z), creal(z)) , 91and similarly for 92.Fn cargf 93and 94.Fn cargl . 95.Sh RETURN VALUES 96The 97.Fn atan2 , 98.Fn atan2f , 99and 100.Fn atan2l 101functions, if successful, 102return the arc tangent of 103.Fa y/ Ns Ar x 104in the range 105.Bk -words 106.Bq \&- Ns \*(Pi , \&+ Ns \*(Pi 107.Ek 108radians. 109Here are some of the special cases: 110.Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___ 111.It Fn atan2 y x No := Ta 112.Fn atan y/x Ta 113if 114.Ar x 115> 0, 116.It Ta sign( Ns Ar y Ns )*(\*(Pi - 117.Fn atan "\\*(Bay/x\\*(Ba" ) Ta 118if 119.Ar x 120< 0, 121.It Ta 122.No 0 Ta 123if x = y = 0, or 124.It Ta 125.Pf sign( Ar y Ns )*\\*(Pi/2 Ta 126if 127.Ar x 128= 0 \(!= 129.Ar y . 130.El 131.Sh NOTES 132The function 133.Fn atan2 134defines "if x > 0," 135.Fn atan2 0 0 136= 0 despite that previously 137.Fn atan2 0 0 138may have generated an error message. 139The reasons for assigning a value to 140.Fn atan2 0 0 141are these: 142.Bl -enum -offset indent 143.It 144Programs that test arguments to avoid computing 145.Fn atan2 0 0 146must be indifferent to its value. 147Programs that require it to be invalid are vulnerable 148to diverse reactions to that invalidity on diverse computer systems. 149.It 150The 151.Fn atan2 152function is used mostly to convert from rectangular (x,y) 153to polar 154.if n\ 155(r,theta) 156.if t\ 157(r,\(*h) 158coordinates that must satisfy x = 159.if n\ 160r\(**cos theta 161.if t\ 162r\(**cos\(*h 163and y = 164.if n\ 165r\(**sin theta. 166.if t\ 167r\(**sin\(*h. 168These equations are satisfied when (x=0,y=0) 169is mapped to 170.if n \ 171(r=0,theta=0). 172.if t \ 173(r=0,\(*h=0). 174In general, conversions to polar coordinates 175should be computed thus: 176.Bd -unfilled -offset indent 177.if n \{\ 178r := hypot(x,y); ... := sqrt(x\(**x+y\(**y) 179theta := atan2(y,x). 180.\} 181.if t \{\ 182r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d) 183\(*h := atan2(y,x). 184.\} 185.Ed 186.It 187The foregoing formulas need not be altered to cope in a 188reasonable way with signed zeros and infinities 189on a machine that conforms to 190.Tn IEEE 754 ; 191the versions of 192.Xr hypot 3 193and 194.Fn atan2 195provided for 196such a machine are designed to handle all cases. 197That is why 198.Fn atan2 \(+-0 \-0 199= \(+-\*(Pi 200for instance. 201In general the formulas above are equivalent to these: 202.Bd -unfilled -offset indent 203.if n \ 204r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x); 205.if t \ 206r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x); 207.Ed 208.El 209.Sh SEE ALSO 210.Xr acos 3 , 211.Xr asin 3 , 212.Xr atan 3 , 213.Xr cabs 3 , 214.Xr cos 3 , 215.Xr cosh 3 , 216.Xr math 3 , 217.Xr sin 3 , 218.Xr sinh 3 , 219.Xr tan 3 , 220.Xr tanh 3 221.Sh STANDARDS 222The 223.Fn atan2 , 224.Fn atan2f , 225.Fn atan2l , 226.Fn carg , 227.Fn cargf , 228and 229.Fn cargl 230functions conform to 231.St -isoC-99 . 232