NAME

std::atan2,std::atan2f,std::atan2l - std::atan2,std::atan2f,std::atan2l

Synopsis

Defined in header <cmath>
float atan2 ( float y, float x );
float atan2f( float y, float x ); (since C++11)
double atan2 ( double y, double x ); (2)
long double atan2 ( long double y, long double x (1)
);
long double atan2l( long double y, long double x (3) (since C++11)
);
Promoted atan2 ( Arithmetic1 y, Arithmetic2 x ); (4) (since C++11)

1-3) Computes the arc tangent of y/x using the signs of arguments to determine the
correct quadrant.
4) A set of overloads or a function template for all combinations of arguments of
arithmetic type not covered by 1-3). If any argument has integral type, it is cast
to double. If any argument is long double, then the return type Promoted is also
long double, otherwise the return type is always double.

Parameters

y, x - values of floating-point or integral types

Return value

If no errors occur, the arc tangent of y/x (arctan(

y
x

)) in the range [-π , +π] radians, is returned.
Y argument

Return value

X argument

If a domain error occurs, an implementation-defined value is returned (NaN where
supported)

If a range error occurs due to underflow, the correct result (after rounding) is
returned.

Error handling

Errors are reported as specified in math_errhandling.

Domain error may occur if x and y are both zero.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

* If x and y are both zero, domain error does not occur
* If x and y are both zero, range error does not occur either
* If y is zero, pole error does not occur
* If y is ±0 and x is negative or -0, ±π is returned
* If y is ±0 and x is positive or +0, ±0 is returned
* If y is ±∞ and x is finite, ±π/2 is returned
* If y is ±∞ and x is -∞, ±3π/4 is returned
* If y is ±∞ and x is +∞, ±π/4 is returned
* If x is ±0 and y is negative, -π/2 is returned
* If x is ±0 and y is positive, +π/2 is returned
* If x is -∞ and y is finite and positive, +π is returned
* If x is -∞ and y is finite and negative, -π is returned
* If x is +∞ and y is finite and positive, +0 is returned
* If x is +∞ and y is finite and negative, -0 is returned
* If either x is NaN or y is NaN, NaN is returned

Notes

std::atan2(y, x) is equivalent to std::arg(std::complex<double>(x,y))

POSIX specifies that in case of underflow, y/x is the value returned, and if that is
not supported, an implementation-defined value no greater than DBL_MIN, FLT_MIN, and
LDBL_MIN is returned.

Example

// Run this code

#include <iostream>
#include <cmath>

int main()
{
// normal usage: the signs of the two arguments determine the quadrant
std::cout << "(x:+1,y:+1) cartesian is (r:" << hypot(1,1)
<< ",phi:" << atan2(1,1) << ") polar\n" // atan2(1,1) = +pi/4, Quad I
<< "(x:-1,y:+1) cartesian is (r:" << hypot(1,-1)
<< ",phi:" << atan2(1,-1) << ") polar\n" // atan2(1, -1) = +3pi/4, Quad II
<< "(x:-1,y:-1) cartesian is (r:" << hypot(-1,-1)
<< ",phi:" << atan2(-1,-1) << ") polar\n" // atan2(-1,-1) = -3pi/4, Quad III
<< "(x:+1,y:-1) cartesian is (r:" << hypot(-1,1)
<< ",phi:" << atan2(-1,1) << ") polar\n"; // atan2(-1, 1) = -pi/4, Quad IV
// special values
std::cout << "atan2(0, 0) = " << atan2(0,0)
<< " atan2(0,-0) = " << atan2(0,-0.0) << '\n'
<< "atan2(7, 0) = " << atan2(7,0)
<< " atan2(7,-0) = " << atan2(7,-0.0) << '\n';
}

Output:

(x:+1,y:+1) cartesian is (r:1.41421,phi:0.785398) polar
(x:-1,y:+1) cartesian is (r:1.41421,phi:2.35619) polar
(x:-1,y:-1) cartesian is (r:1.41421,phi:-2.35619) polar
(x:+1,y:-1) cartesian is (r:1.41421,phi:-0.785398) polar
atan2(0, 0) = 0 atan2(0,-0) = 3.14159
atan2(7, 0) = 1.5708 atan2(7,-0) = 1.5708