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. 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.
19.\"
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
30.\" SUCH DAMAGE.
31.\"
32.\" from: @(#)atan2.3 5.1 (Berkeley) 5/2/91
| 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. 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.
19.\"
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
30.\" SUCH DAMAGE.
31.\"
32.\" from: @(#)atan2.3 5.1 (Berkeley) 5/2/91
|
33.\" $Id: atan2.3,v 1.3 1993/08/14 13:42:32 mycroft Exp $
| 33.\" $Id: atan2.3,v 1.1.1.1 1994/08/19 09:39:41 jkh Exp $
|
34.\"
35.Dd May 2, 1991
36.Dt ATAN2 3
37.Os
38.Sh NAME
| 34.\"
35.Dd May 2, 1991
36.Dt ATAN2 3
37.Os
38.Sh NAME
|
39.Nm atan2
40.Nd arc tangent function of two variables
| 39.Nm atan2 ,
40.Nm atan2f
41.Nd arc tangent functions of two variables
|
41.Sh SYNOPSIS
42.Fd #include <math.h>
43.Ft double
44.Fn atan2 "double y" "double x"
| 42.Sh SYNOPSIS
43.Fd #include <math.h>
44.Ft double
45.Fn atan2 "double y" "double x"
|
| 46.Ft float
47.Fn atan2f "float y" "float x"
|
45.Sh DESCRIPTION
46The
| 48.Sh DESCRIPTION
49The
|
47.Xr atan2
48function computes the principal value of the arc tangent of
49.Ar y/ Ns Ar x ,
| 50.Fn atan2
51and the
52.Fn atan2f
53functions compute the principal value of the arc tangent of
54.Fa y/ Ns Ar x ,
|
50using the signs of both arguments to determine the quadrant of
51the return value.
52.Sh RETURN VALUES
53The
| 55using the signs of both arguments to determine the quadrant of
56the return value.
57.Sh RETURN VALUES
58The
|
54.Xr atan2
55function, if successful,
56returns the arc tangent of
57.Ar y/ Ns Ar x
| 59.Fn atan2
60and the
61.Fn atan2f
62functions, if successful,
63return the arc tangent of
64.Fa y/ Ns Ar x
|
58in the range
59.Bk -words
60.Bq \&- Ns \*(Pi , \&+ Ns \*(Pi
61.Ek
62radians.
63If both
| 65in the range
66.Bk -words
67.Bq \&- Ns \*(Pi , \&+ Ns \*(Pi
68.Ek
69radians.
70If both
|
64.Ar x
| 71.Fa x
|
65and
| 72and
|
66.Ar y
| 73.Fa y
|
67are zero, the global variable
68.Va errno
69is set to
70.Er EDOM .
71On the
72.Tn VAX :
73.Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___
74.It Fn atan2 y x No := Ta
75.Fn atan y/x Ta
76if
77.Ar x
78> 0,
79.It Ta sign( Ns Ar y Ns )*(\*(Pi -
80.Fn atan "\\*(Bay/x\\*(Ba" ) Ta
81if
82.Ar x
83< 0,
84.It Ta
85.No 0 Ta
86if x = y = 0, or
87.It Ta
88.Pf sign( Ar y Ns )*\\*(Pi/2 Ta
89if
90.Ar x
91= 0 \*(!=
92.Ar y .
93.El
94.Sh NOTES
95The function
96.Fn atan2
97defines "if x > 0,"
98.Fn atan2 0 0
99= 0 on a
100.Tn VAX
101despite that previously
102.Fn atan2 0 0
103may have generated an error message.
104The reasons for assigning a value to
105.Fn atan2 0 0
106are these:
107.Bl -enum -offset indent
108.It
109Programs that test arguments to avoid computing
110.Fn atan2 0 0
111must be indifferent to its value.
112Programs that require it to be invalid are vulnerable
113to diverse reactions to that invalidity on diverse computer systems.
114.It
115The
116.Fn atan2
117function is used mostly to convert from rectangular (x,y)
118to polar
119.if n\
120(r,theta)
121.if t\
122(r,\(*h)
123coordinates that must satisfy x =
124.if n\
125r\(**cos theta
126.if t\
127r\(**cos\(*h
128and y =
129.if n\
130r\(**sin theta.
131.if t\
132r\(**sin\(*h.
133These equations are satisfied when (x=0,y=0)
134is mapped to
135.if n \
136(r=0,theta=0)
137.if t \
138(r=0,\(*h=0)
139on a VAX. In general, conversions to polar coordinates
140should be computed thus:
141.Bd -unfilled -offset indent
142.if n \{\
143r := hypot(x,y); ... := sqrt(x\(**x+y\(**y)
144theta := atan2(y,x).
145.\}
146.if t \{\
147r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d)
148\(*h := atan2(y,x).
149.\}
150.Ed
151.It
152The foregoing formulas need not be altered to cope in a
153reasonable way with signed zeros and infinities
154on a machine that conforms to
155.Tn IEEE 754 ;
156the versions of
157.Xr hypot 3
158and
159.Fn atan2
160provided for
161such a machine are designed to handle all cases.
162That is why
163.Fn atan2 \(+-0 \-0
164= \(+-\*(Pi
165for instance.
166In general the formulas above are equivalent to these:
167.Bd -unfilled -offset indent
168.if n \
169r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x);
170.if t \
171r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x);
172.Ed
173.El
174.Sh SEE ALSO
175.Xr acos 3 ,
176.Xr asin 3 ,
177.Xr atan 3 ,
178.Xr cos 3 ,
179.Xr cosh 3 ,
180.Xr sin 3 ,
181.Xr sinh 3 ,
182.Xr tan 3 ,
183.Xr tanh 3 ,
184.Xr math 3 ,
185.Sh STANDARDS
186The
187.Fn atan2
188function conforms to
189.St -ansiC .
| 74are zero, the global variable
75.Va errno
76is set to
77.Er EDOM .
78On the
79.Tn VAX :
80.Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___
81.It Fn atan2 y x No := Ta
82.Fn atan y/x Ta
83if
84.Ar x
85> 0,
86.It Ta sign( Ns Ar y Ns )*(\*(Pi -
87.Fn atan "\\*(Bay/x\\*(Ba" ) Ta
88if
89.Ar x
90< 0,
91.It Ta
92.No 0 Ta
93if x = y = 0, or
94.It Ta
95.Pf sign( Ar y Ns )*\\*(Pi/2 Ta
96if
97.Ar x
98= 0 \*(!=
99.Ar y .
100.El
101.Sh NOTES
102The function
103.Fn atan2
104defines "if x > 0,"
105.Fn atan2 0 0
106= 0 on a
107.Tn VAX
108despite that previously
109.Fn atan2 0 0
110may have generated an error message.
111The reasons for assigning a value to
112.Fn atan2 0 0
113are these:
114.Bl -enum -offset indent
115.It
116Programs that test arguments to avoid computing
117.Fn atan2 0 0
118must be indifferent to its value.
119Programs that require it to be invalid are vulnerable
120to diverse reactions to that invalidity on diverse computer systems.
121.It
122The
123.Fn atan2
124function is used mostly to convert from rectangular (x,y)
125to polar
126.if n\
127(r,theta)
128.if t\
129(r,\(*h)
130coordinates that must satisfy x =
131.if n\
132r\(**cos theta
133.if t\
134r\(**cos\(*h
135and y =
136.if n\
137r\(**sin theta.
138.if t\
139r\(**sin\(*h.
140These equations are satisfied when (x=0,y=0)
141is mapped to
142.if n \
143(r=0,theta=0)
144.if t \
145(r=0,\(*h=0)
146on a VAX. In general, conversions to polar coordinates
147should be computed thus:
148.Bd -unfilled -offset indent
149.if n \{\
150r := hypot(x,y); ... := sqrt(x\(**x+y\(**y)
151theta := atan2(y,x).
152.\}
153.if t \{\
154r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d)
155\(*h := atan2(y,x).
156.\}
157.Ed
158.It
159The foregoing formulas need not be altered to cope in a
160reasonable way with signed zeros and infinities
161on a machine that conforms to
162.Tn IEEE 754 ;
163the versions of
164.Xr hypot 3
165and
166.Fn atan2
167provided for
168such a machine are designed to handle all cases.
169That is why
170.Fn atan2 \(+-0 \-0
171= \(+-\*(Pi
172for instance.
173In general the formulas above are equivalent to these:
174.Bd -unfilled -offset indent
175.if n \
176r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x);
177.if t \
178r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x);
179.Ed
180.El
181.Sh SEE ALSO
182.Xr acos 3 ,
183.Xr asin 3 ,
184.Xr atan 3 ,
185.Xr cos 3 ,
186.Xr cosh 3 ,
187.Xr sin 3 ,
188.Xr sinh 3 ,
189.Xr tan 3 ,
190.Xr tanh 3 ,
191.Xr math 3 ,
192.Sh STANDARDS
193The
194.Fn atan2
195function conforms to
196.St -ansiC .
|