1 .\" Copyright (c) 1991 The Regents of the University of California.
2 .\" All rights reserved.
4 .\" Redistribution and use in source and binary forms, with or without
5 .\" modification, are permitted provided that the following conditions
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.
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
32 .\" from: @(#)atan2.3 5.1 (Berkeley) 5/2/91
33 .\" $FreeBSD: src/lib/msun/man/atan2.3,v 1.6.2.4 2001/12/17 10:08:36 ru Exp $
41 .Nd arc tangent functions of two variables
47 .Fn atan2 "double y" "double x"
49 .Fn atan2f "float y" "float x"
55 functions compute the principal value of the arc tangent of
57 using the signs of both arguments to determine the quadrant of
64 functions, if successful,
65 return the arc tangent of
69 .Bq \&- Ns \*(Pi , \&+ Ns \*(Pi
76 are zero, the global variable
82 .Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___
83 .It Fn atan2 y x No := Ta
88 .It Ta sign( Ns Ar y Ns )*(\*(Pi -
89 .Fn atan "\\*(Bay/x\\*(Ba" ) Ta
97 .Pf sign( Ar y Ns )*\\*(Pi/2 Ta
110 despite that previously
112 may have generated an error message.
113 The reasons for assigning a value to
116 .Bl -enum -offset indent
118 Programs that test arguments to avoid computing
120 must be indifferent to its value.
121 Programs that require it to be invalid are vulnerable
122 to diverse reactions to that invalidity on diverse computer systems.
126 function is used mostly to convert from rectangular (x,y)
132 coordinates that must satisfy x =
142 These equations are satisfied when (x=0,y=0)
148 on a VAX. In general, conversions to polar coordinates
149 should be computed thus:
150 .Bd -unfilled -offset indent
152 r := hypot(x,y); ... := sqrt(x\(**x+y\(**y)
156 r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d)
161 The foregoing formulas need not be altered to cope in a
162 reasonable way with signed zeros and infinities
163 on a machine that conforms to
170 such a machine are designed to handle all cases.
175 In general the formulas above are equivalent to these:
176 .Bd -unfilled -offset indent
178 r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x);
180 r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x);