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 December 12, 2007 32.Dt ATAN2 3 33.Os 34.Sh NAME 35.Nm atan2 , 36.Nm atan2f , 37.Nm carg , 38.Nm cargf 39.Nd arc tangent and complex phase angle functions 40.Sh LIBRARY 41.Lb libm 42.Sh SYNOPSIS 43.In math.h 44.Ft double 45.Fn atan2 "double y" "double x" 46.Ft float 47.Fn atan2f "float y" "float x" 48.Ft double 49.Fn carg "double complex z" 50.Ft float 51.Fn cargf "float complex z" 52.Sh DESCRIPTION 53The 54.Fn atan2 55and the 56.Fn atan2f 57functions compute the principal value of the arc tangent of 58.Fa y/ Ns Ar x , 59using the signs of both arguments to determine the quadrant of 60the return value. 61.ie '\*[.T]'utf8' \{\ 62. ds Th \[*h] 63.\} 64.el \{\ 65. ds Th theta 66.\} 67.Pp 68The 69.Fn carg 70and 71.Fn cargf 72functions compute the complex argument (or phase angle) of 73.Fa z . 74The complex argument is the number \*(Th such that 75.Li z = r * e^(I * \*(Th) , 76where 77.Li r = cabs(z) . 78The call 79.Li carg(z) 80is equivalent to 81.Li atan2(cimag(z), creal(z)) , 82and similarly for 83.Fn cargf . 84.Sh RETURN VALUES 85The 86.Fn atan2 87and the 88.Fn atan2f 89functions, if successful, 90return the arc tangent of 91.Fa y/ Ns Ar x 92in the range 93.Bk -words 94.Bq \&- Ns \*(Pi , \&+ Ns \*(Pi 95.Ek 96radians. 97Here are some of the special cases: 98.Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___ 99.It Fn atan2 y x No := Ta 100.Fn atan y/x Ta 101if 102.Ar x 103> 0, 104.It Ta sign( Ns Ar y Ns )*(\*(Pi - 105.Fn atan "\\*(Bay/x\\*(Ba" ) Ta 106if 107.Ar x 108< 0, 109.It Ta 110.No 0 Ta 111if x = y = 0, or 112.It Ta 113.Pf sign( Ar y Ns )*\\*(Pi/2 Ta 114if 115.Ar x 116= 0 \(!= 117.Ar y . 118.El 119.Sh NOTES 120The function 121.Fn atan2 122defines "if x > 0," 123.Fn atan2 0 0 124= 0 despite that previously 125.Fn atan2 0 0 126may have generated an error message. 127The reasons for assigning a value to 128.Fn atan2 0 0 129are these: 130.Bl -enum -offset indent 131.It 132Programs that test arguments to avoid computing 133.Fn atan2 0 0 134must be indifferent to its value. 135Programs that require it to be invalid are vulnerable 136to diverse reactions to that invalidity on diverse computer systems. 137.It 138The 139.Fn atan2 140function is used mostly to convert from rectangular (x,y) 141to polar 142.if n\ 143(r,theta) 144.if t\ 145(r,\(*h) 146coordinates that must satisfy x = 147.if n\ 148r\(**cos theta 149.if t\ 150r\(**cos\(*h 151and y = 152.if n\ 153r\(**sin theta. 154.if t\ 155r\(**sin\(*h. 156These equations are satisfied when (x=0,y=0) 157is mapped to 158.if n \ 159(r=0,theta=0). 160.if t \ 161(r=0,\(*h=0). 162In general, conversions to polar coordinates 163should be computed thus: 164.Bd -unfilled -offset indent 165.if n \{\ 166r := hypot(x,y); ... := sqrt(x\(**x+y\(**y) 167theta := atan2(y,x). 168.\} 169.if t \{\ 170r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d) 171\(*h := atan2(y,x). 172.\} 173.Ed 174.It 175The foregoing formulas need not be altered to cope in a 176reasonable way with signed zeros and infinities 177on a machine that conforms to 178.Tn IEEE 754 ; 179the versions of 180.Xr hypot 3 181and 182.Fn atan2 183provided for 184such a machine are designed to handle all cases. 185That is why 186.Fn atan2 \(+-0 \-0 187= \(+-\*(Pi 188for instance. 189In general the formulas above are equivalent to these: 190.Bd -unfilled -offset indent 191.if n \ 192r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x); 193.if t \ 194r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x); 195.Ed 196.El 197.Sh SEE ALSO 198.Xr acos 3 , 199.Xr asin 3 , 200.Xr atan 3 , 201.Xr cabs 3 , 202.Xr cos 3 , 203.Xr cosh 3 , 204.Xr math 3 , 205.Xr sin 3 , 206.Xr sinh 3 , 207.Xr tan 3 , 208.Xr tanh 3 209.Sh STANDARDS 210The 211.Fn atan2 , 212.Fn atan2f , 213.Fn carg , 214and 215.Fn cargf 216functions conform to 217.St -isoC-99 . 218