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28 .\" from: @(#)atan2.3 5.1 (Berkeley) 5/2/91
41 .Nd arc tangent and complex phase angle functions
47 .Fn atan2 "double y" "double x"
49 .Fn atan2f "float y" "float x"
51 .Fn atan2l "long double y" "long double x"
54 .Fn carg "double complex z"
56 .Fn cargf "float complex z"
58 .Fn cargl "long double complex z"
65 functions compute the principal value of the arc tangent of
67 using the signs of both arguments to determine the quadrant of
75 functions compute the complex argument (or phase angle) of
77 The complex argument is the number theta such that
78 .Li z = r * e^(I * theta) ,
84 .Li atan2(cimag(z), creal(z)) ,
95 functions, if successful,
96 return the arc tangent of
100 .Bq \&- Ns \*(Pi , \&+ Ns \*(Pi
103 Here are some of the special cases:
104 .Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___
105 .It Fn atan2 y x No := Ta
110 .It Ta sign( Ns Ar y Ns )*(\*(Pi -
111 .Fn atan "\*(Bay/x\*(Ba" ) Ta
119 .Pf sign( Ar y Ns )*\*(Pi/2 Ta
130 = 0 despite that previously
132 may have generated an error message.
133 The reasons for assigning a value to
136 .Bl -enum -offset indent
138 Programs that test arguments to avoid computing
140 must be indifferent to its value.
141 Programs that require it to be invalid are vulnerable
142 to diverse reactions to that invalidity on diverse computer systems.
146 function is used mostly to convert from rectangular (x,y)
152 coordinates that must satisfy x =
162 These equations are satisfied when (x=0,y=0)
168 In general, conversions to polar coordinates
169 should be computed thus:
170 .Bd -unfilled -offset indent
172 r := hypot(x,y); ... := sqrt(x\(**x+y\(**y)
176 r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d)
181 The foregoing formulas need not be altered to cope in a
182 reasonable way with signed zeros and infinities
183 on a machine that conforms to
190 such a machine are designed to handle all cases.
195 In general the formulas above are equivalent to these:
196 .Bd -unfilled -offset indent
198 r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x);
200 r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x);