ATAN2(3) BSD Library Functions Manual ATAN2(3)
atan2, atan2f -- arc tangent function of two variables
Math Library (libm, -lm)
atan2(double y, double x);
atan2f(float y, float x);
The atan2() and atan2f() functions compute the principal value of the arc
tangent of y/x, using the signs of both arguments to determine the quad-
rant of the return value.
The atan2() function, if successful, returns the arc tangent of y/x in
the range [-pi, +pi] radians. If both x and y are zero, the global vari-
able errno is set to EDOM. On the VAX:
atan2(y, x) := atan(y/x) if x > 0,
sign(y)*(pi - atan(|y/x|)) if x < 0,
0 if x = y = 0, or
sign(y)*pi/2 if x = 0 y.
The function atan2() defines "if x > 0," atan2(0, 0) = 0 on a VAX despite
that previously atan2(0, 0) may have generated an error message. The
reasons for assigning a value to atan2(0, 0) are these:
1. Programs that test arguments to avoid computing atan2(0, 0)
must be indifferent to its value. Programs that require it to
be invalid are vulnerable to diverse reactions to that inva-
lidity on diverse computer systems.
2. The atan2() function is used mostly to convert from rectangu-
lar (x,y) to polar (r,theta) coordinates that must satisfy x =
r*cos theta and y = r*sin theta. These equations are satis-
fied when (x=0,y=0) is mapped to (r=0,theta=0) on a VAX. In
general, conversions to polar coordinates should be computed
r := hypot(x,y); ... := sqrt(x*x+y*y)
theta := atan2(y,x).
3. The foregoing formulas need not be altered to cope in a rea-
sonable way with signed zeros and infinities on a machine that
conforms to IEEE 754; the versions of hypot(3) and atan2()
provided for such a machine are designed to handle all cases.
That is why atan2(+-0, -0) = +-pi 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);
acos(3), asin(3), atan(3), cos(3), cosh(3), math(3), sin(3), sinh(3),
The atan2() function conforms to ANSI X3.159-1989 (``ANSI C89'').
BSD May 2, 1991 BSD