xref: /freebsd/lib/msun/man/atan2.3 (revision 282a3889ebf826db9839be296ff1dd903f6d6d6e)
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28.\"     from: @(#)atan2.3	5.1 (Berkeley) 5/2/91
29.\" $FreeBSD$
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31.Dd January 14, 2005
32.Dt ATAN2 3
33.Os
34.Sh NAME
35.Nm atan2 ,
36.Nm atan2f
37.Nd arc tangent functions of two variables
38.Sh LIBRARY
39.Lb libm
40.Sh SYNOPSIS
41.In math.h
42.Ft double
43.Fn atan2 "double y" "double x"
44.Ft float
45.Fn atan2f "float y" "float x"
46.Sh DESCRIPTION
47The
48.Fn atan2
49and the
50.Fn atan2f
51functions compute the principal value of the arc tangent of
52.Fa y/ Ns Ar x ,
53using the signs of both arguments to determine the quadrant of
54the return value.
55.Sh RETURN VALUES
56The
57.Fn atan2
58and the
59.Fn atan2f
60functions, if successful,
61return the arc tangent of
62.Fa y/ Ns Ar x
63in the range
64.Bk -words
65.Bq \&- Ns \*(Pi , \&+ Ns \*(Pi
66.Ek
67radians.
68Here are some of the special cases:
69.Bl -column atan_(y,x)_:=____  sign(y)_(Pi_atan2(Xy_xX))___
70.It Fn atan2 y x No := Ta
71.Fn atan y/x Ta
72if
73.Ar x
74> 0,
75.It Ta sign( Ns Ar y Ns )*(\*(Pi -
76.Fn atan "\\*(Bay/x\\*(Ba" ) Ta
77if
78.Ar x
79< 0,
80.It Ta
81.No 0 Ta
82if x = y = 0, or
83.It Ta
84.Pf sign( Ar y Ns )*\\*(Pi/2 Ta
85if
86.Ar x
87= 0 \(!=
88.Ar y .
89.El
90.Sh NOTES
91The function
92.Fn atan2
93defines "if x > 0,"
94.Fn atan2 0 0
95= 0 despite that previously
96.Fn atan2 0 0
97may have generated an error message.
98The reasons for assigning a value to
99.Fn atan2 0 0
100are these:
101.Bl -enum -offset indent
102.It
103Programs that test arguments to avoid computing
104.Fn atan2 0 0
105must be indifferent to its value.
106Programs that require it to be invalid are vulnerable
107to diverse reactions to that invalidity on diverse computer systems.
108.It
109The
110.Fn atan2
111function is used mostly to convert from rectangular (x,y)
112to polar
113.if n\
114(r,theta)
115.if t\
116(r,\(*h)
117coordinates that must satisfy x =
118.if n\
119r\(**cos theta
120.if t\
121r\(**cos\(*h
122and y =
123.if n\
124r\(**sin theta.
125.if t\
126r\(**sin\(*h.
127These equations are satisfied when (x=0,y=0)
128is mapped to
129.if n \
130(r=0,theta=0).
131.if t \
132(r=0,\(*h=0).
133In general, conversions to polar coordinates
134should be computed thus:
135.Bd -unfilled -offset indent
136.if n \{\
137r	:= hypot(x,y);  ... := sqrt(x\(**x+y\(**y)
138theta	:= atan2(y,x).
139.\}
140.if t \{\
141r	:= hypot(x,y);  ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d)
142\(*h	:= atan2(y,x).
143.\}
144.Ed
145.It
146The foregoing formulas need not be altered to cope in a
147reasonable way with signed zeros and infinities
148on a machine that conforms to
149.Tn IEEE 754 ;
150the versions of
151.Xr hypot 3
152and
153.Fn atan2
154provided for
155such a machine are designed to handle all cases.
156That is why
157.Fn atan2 \(+-0 \-0
158= \(+-\*(Pi
159for instance.
160In general the formulas above are equivalent to these:
161.Bd -unfilled -offset indent
162.if n \
163r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x);
164.if t \
165r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x);
166.Ed
167.El
168.Sh SEE ALSO
169.Xr acos 3 ,
170.Xr asin 3 ,
171.Xr atan 3 ,
172.Xr cos 3 ,
173.Xr cosh 3 ,
174.Xr math 3 ,
175.Xr sin 3 ,
176.Xr sinh 3 ,
177.Xr tan 3 ,
178.Xr tanh 3
179.Sh STANDARDS
180The
181.Fn atan2
182function conforms to
183.St -isoC .
184