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.Dd July 31, 2008 29.Dt ATAN2 3 30.Os 31.Sh NAME 32.Nm atan2 , 33.Nm atan2f , 34.Nm atan2l , 35.Nm carg , 36.Nm cargf , 37.Nm cargl 38.Nd arc tangent and complex phase angle functions 39.Sh LIBRARY 40.Lb libm 41.Sh SYNOPSIS 42.In math.h 43.Ft double 44.Fn atan2 "double y" "double x" 45.Ft float 46.Fn atan2f "float y" "float x" 47.Ft long double 48.Fn atan2l "long double y" "long double x" 49.In complex.h 50.Ft double 51.Fn carg "double complex z" 52.Ft float 53.Fn cargf "float complex z" 54.Ft long double 55.Fn cargl "long double complex z" 56.Sh DESCRIPTION 57The 58.Fn atan2 , 59.Fn atan2f , 60and 61.Fn atan2l 62functions compute the principal value of the arc tangent of 63.Fa y/ Ns Fa x , 64using the signs of both arguments to determine the quadrant of 65the return value. 66.Pp 67The 68.Fn carg , 69.Fn cargf , 70and 71.Fn cargl 72functions compute the complex argument (or phase angle) of 73.Fa z . 74The complex argument is the number theta such that 75.Li z = r * e^(I * theta) , 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 84and 85.Fn cargl . 86.Sh RETURN VALUES 87The 88.Fn atan2 , 89.Fn atan2f , 90and 91.Fn atan2l 92functions, if successful, 93return the arc tangent of 94.Fa y/ Ns Fa x 95in the range 96.Bk -words 97.Bq \&- Ns \*(Pi , \&+ Ns \*(Pi 98.Ek 99radians. 100Here are some of the special cases: 101.Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___ 102.It Fn atan2 y x No := Ta 103.Fn atan y/x Ta 104if 105.Fa x 106> 0, 107.It Ta sign( Ns Fa y Ns )*(\*(Pi - 108.Fn atan "\*(Bay/x\*(Ba" ) Ta 109if 110.Fa x 111< 0, 112.It Ta 113.No 0 Ta 114if x = y = 0, or 115.It Ta 116.Pf sign( Fa y Ns )*\*(Pi/2 Ta 117if 118.Fa x 119= 0 \(!= 120.Fa y . 121.El 122.Sh NOTES 123The function 124.Fn atan2 125defines "if x > 0," 126.Fn atan2 0 0 127= 0 despite that previously 128.Fn atan2 0 0 129may have generated an error message. 130The reasons for assigning a value to 131.Fn atan2 0 0 132are these: 133.Bl -enum -offset indent 134.It 135Programs that test arguments to avoid computing 136.Fn atan2 0 0 137must be indifferent to its value. 138Programs that require it to be invalid are vulnerable 139to diverse reactions to that invalidity on diverse computer systems. 140.It 141The 142.Fn atan2 143function is used mostly to convert from rectangular (x,y) 144to polar 145.if n\ 146(r,theta) 147.if t\ 148(r,\(*h) 149coordinates that must satisfy x = 150.if n\ 151r\(**cos theta 152.if t\ 153r\(**cos\(*h 154and y = 155.if n\ 156r\(**sin theta. 157.if t\ 158r\(**sin\(*h. 159These equations are satisfied when (x=0,y=0) 160is mapped to 161.if n \ 162(r=0,theta=0). 163.if t \ 164(r=0,\(*h=0). 165In general, conversions to polar coordinates 166should be computed thus: 167.Bd -unfilled -offset indent 168.if n \{\ 169r := hypot(x,y); ... := sqrt(x\(**x+y\(**y) 170theta := atan2(y,x). 171.\} 172.if t \{\ 173r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d) 174\(*h := atan2(y,x). 175.\} 176.Ed 177.It 178The foregoing formulas need not be altered to cope in a 179reasonable way with signed zeros and infinities 180on a machine that conforms to 181.Tn IEEE 754 ; 182the versions of 183.Xr hypot 3 184and 185.Fn atan2 186provided for 187such a machine are designed to handle all cases. 188That is why 189.Fn atan2 \(+-0 \-0 190= \(+-\*(Pi 191for instance. 192In general the formulas above are equivalent to these: 193.Bd -unfilled -offset indent 194.if n \ 195r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x); 196.if t \ 197r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x); 198.Ed 199.El 200.Sh SEE ALSO 201.Xr acos 3 , 202.Xr asin 3 , 203.Xr atan 3 , 204.Xr cabs 3 , 205.Xr cos 3 , 206.Xr cosh 3 , 207.Xr math 3 , 208.Xr sin 3 , 209.Xr sinh 3 , 210.Xr tan 3 , 211.Xr tanh 3 212.Sh STANDARDS 213The 214.Fn atan2 , 215.Fn atan2f , 216.Fn atan2l , 217.Fn carg , 218.Fn cargf , 219and 220.Fn cargl 221functions conform to 222.St -isoC-99 . 223