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. 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.Pp 70The 71.Fn carg , 72.Fn cargf , 73and 74.Fn cargl 75functions compute the complex argument (or phase angle) of 76.Fa z . 77The complex argument is the number theta such that 78.Li z = r * e^(I * theta) , 79where 80.Li r = cabs(z) . 81The call 82.Li carg(z) 83is equivalent to 84.Li atan2(cimag(z), creal(z)) , 85and similarly for 86.Fn cargf 87and 88.Fn cargl . 89.Sh RETURN VALUES 90The 91.Fn atan2 , 92.Fn atan2f , 93and 94.Fn atan2l 95functions, if successful, 96return the arc tangent of 97.Fa y/ Ns Ar x 98in the range 99.Bk -words 100.Bq \&- Ns \*(Pi , \&+ Ns \*(Pi 101.Ek 102radians. 103Here are some of the special cases: 104.Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___ 105.It Fn atan2 y x No := Ta 106.Fn atan y/x Ta 107if 108.Ar x 109> 0, 110.It Ta sign( Ns Ar y Ns )*(\*(Pi - 111.Fn atan "\*(Bay/x\*(Ba" ) Ta 112if 113.Ar x 114< 0, 115.It Ta 116.No 0 Ta 117if x = y = 0, or 118.It Ta 119.Pf sign( Ar y Ns )*\*(Pi/2 Ta 120if 121.Ar x 122= 0 \(!= 123.Ar y . 124.El 125.Sh NOTES 126The function 127.Fn atan2 128defines "if x > 0," 129.Fn atan2 0 0 130= 0 despite that previously 131.Fn atan2 0 0 132may have generated an error message. 133The reasons for assigning a value to 134.Fn atan2 0 0 135are these: 136.Bl -enum -offset indent 137.It 138Programs that test arguments to avoid computing 139.Fn atan2 0 0 140must be indifferent to its value. 141Programs that require it to be invalid are vulnerable 142to diverse reactions to that invalidity on diverse computer systems. 143.It 144The 145.Fn atan2 146function is used mostly to convert from rectangular (x,y) 147to polar 148.if n\ 149(r,theta) 150.if t\ 151(r,\(*h) 152coordinates that must satisfy x = 153.if n\ 154r\(**cos theta 155.if t\ 156r\(**cos\(*h 157and y = 158.if n\ 159r\(**sin theta. 160.if t\ 161r\(**sin\(*h. 162These equations are satisfied when (x=0,y=0) 163is mapped to 164.if n \ 165(r=0,theta=0). 166.if t \ 167(r=0,\(*h=0). 168In general, conversions to polar coordinates 169should be computed thus: 170.Bd -unfilled -offset indent 171.if n \{\ 172r := hypot(x,y); ... := sqrt(x\(**x+y\(**y) 173theta := atan2(y,x). 174.\} 175.if t \{\ 176r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d) 177\(*h := atan2(y,x). 178.\} 179.Ed 180.It 181The foregoing formulas need not be altered to cope in a 182reasonable way with signed zeros and infinities 183on a machine that conforms to 184.Tn IEEE 754 ; 185the versions of 186.Xr hypot 3 187and 188.Fn atan2 189provided for 190such a machine are designed to handle all cases. 191That is why 192.Fn atan2 \(+-0 \-0 193= \(+-\*(Pi 194for instance. 195In general the formulas above are equivalent to these: 196.Bd -unfilled -offset indent 197.if n \ 198r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x); 199.if t \ 200r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x); 201.Ed 202.El 203.Sh SEE ALSO 204.Xr acos 3 , 205.Xr asin 3 , 206.Xr atan 3 , 207.Xr cabs 3 , 208.Xr cos 3 , 209.Xr cosh 3 , 210.Xr math 3 , 211.Xr sin 3 , 212.Xr sinh 3 , 213.Xr tan 3 , 214.Xr tanh 3 215.Sh STANDARDS 216The 217.Fn atan2 , 218.Fn atan2f , 219.Fn atan2l , 220.Fn carg , 221.Fn cargf , 222and 223.Fn cargl 224functions conform to 225.St -isoC-99 . 226