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32 .\" from: @(#)atan2.3 5.1 (Berkeley) 5/2/91
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
72 Here are some of the special cases:
73 .Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___
74 .It Fn atan2 y x No := Ta
79 .It Ta sign( Ns Ar y Ns )*(\*(Pi -
80 .Fn atan "\\*(Bay/x\\*(Ba" ) Ta
88 .Pf sign( Ar y Ns )*\\*(Pi/2 Ta
99 = 0 despite that previously
101 may have generated an error message.
102 The reasons for assigning a value to
105 .Bl -enum -offset indent
107 Programs that test arguments to avoid computing
109 must be indifferent to its value.
110 Programs that require it to be invalid are vulnerable
111 to diverse reactions to that invalidity on diverse computer systems.
115 function is used mostly to convert from rectangular (x,y)
121 coordinates that must satisfy x =
131 These equations are satisfied when (x=0,y=0)
137 In general, conversions to polar coordinates
138 should be computed thus:
139 .Bd -unfilled -offset indent
141 r := hypot(x,y); ... := sqrt(x\(**x+y\(**y)
145 r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d)
150 The foregoing formulas need not be altered to cope in a
151 reasonable way with signed zeros and infinities
152 on a machine that conforms to
159 such a machine are designed to handle all cases.
164 In general the formulas above are equivalent to these:
165 .Bd -unfilled -offset indent
167 r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x);
169 r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x);