Updated: 2021/Apr/14

```ATAN2(3)                   Library Functions Manual                   ATAN2(3)

NAME
atan2, atan2f, atan2l - arc tangent function of two variables

LIBRARY
Math Library (libm, -lm)

SYNOPSIS
#include <math.h>

double
atan2(double y, double x);

float
atan2f(float y, float x);

long double
atan2l(long double y, long double x);

DESCRIPTION
The atan2(), atan2f(), and atan2l() functions compute 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 [-pi, +pi] radians.  If both x and y are zero, the global
variable 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.

NOTES
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
invalidity on diverse computer systems.

2.   The 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).

3.   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
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);