Fd #include <math.h>
Ft double
Fn atan2 double y double x
DESCRIPTION
The
atan2
function computes the principal value of the arc tangent of
y/ x
using the signs of both arguments to determine the quadrant of
the return value.
RETURN VALUES
The
atan2
function, if successful,
returns the arc tangent of
y/ x
in the range
-words
Bq - Ns , + Ns
radians.
If both
x
and
y
are zero, the global variable
errno
is set to
Er EDOM .
On the
VAX
Fn atan2 y x := Ta Fn atan y/x Ta if
x
> 0,
Ta sign( y )*(
Fn atan \*(Bay/x\*(Ba ) Ta
if
x
< 0,
Ta 0 Ta if x = y = 0, or
Ta sign( y )*\*(Pi/2 Ta if
x
= 0
y
NOTES
The function
Fn atan2
defines "if x > 0,"
Fn atan2 0 0
= 0 on a
VAX
despite that previously
Fn atan2 0 0
may have generated an error message.
The reasons for assigning a value to
Fn atan2 0 0
are these:
Programs that test arguments to avoid computing
Fn atan2 0 0
must be indifferent to its value.
Programs that require it to be invalid are vulnerable
to diverse reactions to that invalidity on diverse computer systems.
The
Fn atan2
function is used mostly to convert from rectangular (x,y)
to polar
(r,theta)
coordinates that must satisfy x =
r*cos theta
and y =
r*sin theta.
These equations are satisfied when (x=0,y=0)
is mapped to
(r=0,theta=0)
on a VAX. In general, conversions to polar coordinates
should be computed thus:
r := hypot(x,y); ... := sqrt(x*x+y*y)
theta := atan2(y,x).
The foregoing formulas need not be altered to cope in a
reasonable way with signed zeros and infinities
on a machine that conforms to
IEEE 754
the versions of
hypot(3)
and
Fn atan2
provided for
such a machine are designed to handle all cases.
That is why
Fn atan2 ±0 -0
= ±
for instance.
In general the formulas above are equivalent to these:
r := sqrt(x*x+y*y); if r = 0 then x := copysign(1,x);