xref: /freebsd/lib/msun/man/atan2.3 (revision 1e413cf93298b5b97441a21d9a50fdcd0ee9945e)
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28.\"     from: @(#)atan2.3	5.1 (Berkeley) 5/2/91
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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