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29 .\" from: @(#)atan2.3 5.1 (Berkeley) 5/2/91
31 .Dd $Mdocdate: January 15 2015 $
38 .Nd arc tangent functions of two variables
42 .Fn atan2 "double y" "double x"
44 .Fn atan2f "float y" "float x"
46 .Fn atan2l "long double y" "long double x"
50 function computes the principal value of the arc tangent of
52 using the signs of both arguments to determine the quadrant of
56 function is a single precision version of
60 function is an extended precision version of
68 functions, if successful,
69 return the arc tangent of
73 .Bq \&- Ns \*(Pi , \&+ Ns \*(Pi
80 are zero, the global variable
85 .Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___
86 .It Fn atan2 y x No := Ta
91 .It Ta sign( Ns Ar y Ns )*(\*(Pi -
92 .Fn atan "\*(Bay/x\*(Ba" ) Ta
104 .Pf sign( Ar y Ns )*\*(Pi/2 Ta
116 = 0 on a VAX despite that previously
118 may have generated an error message.
119 The reasons for assigning a value to
122 .Bl -enum -offset indent
124 Programs that test arguments to avoid computing
126 must be indifferent to its value.
127 Programs that require it to be invalid are vulnerable
128 to diverse reactions to that invalidity on diverse computer systems.
132 function is used mostly to convert from rectangular (x,y)
138 coordinates that must satisfy x =
148 These equations are satisfied when (x=0,y=0)
155 In general, conversions to polar coordinates
156 should be computed thus:
157 .Bd -unfilled -offset indent
159 r := hypot(x,y); ... := sqrt(x\(**x+y\(**y)
163 r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d)
168 The foregoing formulas need not be altered to cope in a
169 reasonable way with signed zeros and infinities
170 on a machine that conforms to IEEE 754 ;
176 such a machine are designed to handle all cases.
181 In general the formulas above are equivalent to these:
182 .Bd -unfilled -offset indent
184 r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x);
186 r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x);