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32 .\" @(#)atan2.3 8.1 (Berkeley) 6/4/93
33 .\" $FreeBSD: src/lib/libm/common_source/atan2.3,v 1.5.2.4 2001/07/22 12:07:16 dd Exp $
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41 .Nd arc tangent function of two variables
47 .Fn atan2 "double y" "double x"
51 function computes the principal value of the arc tangent of
53 using the signs of both arguments to determine the quadrant of
58 function, if successful,
59 returns the arc tangent of
63 .Bq \&- Ns \*(Pi , \&+ Ns \*(Pi
70 are zero, the global variable
76 .Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___
77 .It Fn atan2 y x No := Ta
82 .It Ta sign( Ns Ar y Ns )*(\*(Pi -
83 .Fn atan "\\*(Bay/x\\*(Ba" ) Ta
91 .Pf sign( Ar y Ns )*\\*(Pi/2 Ta
104 despite that previously
106 may have generated an error message.
107 The reasons for assigning a value to
110 .Bl -enum -offset indent
112 Programs that test arguments to avoid computing
114 must be indifferent to its value.
115 Programs that require it to be invalid are vulnerable
116 to diverse reactions to that invalidity on diverse computer systems.
120 function is used mostly to convert from rectangular (x,y)
126 coordinates that must satisfy x =
136 These equations are satisfied when (x=0,y=0)
142 on a VAX. In general, conversions to polar coordinates
143 should be computed thus:
144 .Bd -unfilled -offset indent
146 r := hypot(x,y); ... := sqrt(x\(**x+y\(**y)
150 r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d)
155 The foregoing formulas need not be altered to cope in a
156 reasonable way with signed zeros and infinities
157 on a machine that conforms to
164 such a machine are designed to handle all cases.
169 In general the formulas above are equivalent to these:
170 .Bd -unfilled -offset indent
172 r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x);
174 r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x);