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:
- 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.
- 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).
- 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);
SEE ALSO
acos(3),
asin(3),
atan(3),
cos(3),
cosh(3),
math(3),
sin(3),
sinh(3),
tan(3),
tanh(3)
STANDARDS
The
atan2() function conforms to
ISO/IEC
9899:1999 (“ISO C99”).