std::atan2

float       atan2( float y, float x );

double      atan2( double y, double x );

long double atan2( long double y, long double x );

Promoted    atan2( Arithmetic1 y, Arithmetic2 x );

Computes the arc tangent of y/x using the signs of arguments to determine the correct quadrant.

Parameters

Return value

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

)) 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, and implementation-defined value no greater than DBL_MIN, FLT_MIN, and LDBL_MIN is returned.

Example

#include <iostream>
#include <cmath>
 
int main()
{
    // normal usage: the signs of the two arguments determine the quadrant
    std::cout << "(+1,+1) cartesian is (" << hypot(1,1)
              << ',' << atan2(1,1) << ") polar\n"  // atan2(1,1) = +pi/4, Quad I
              << "(+1,-1) cartesian is (" << hypot(1,-1)
              << ',' << atan2(1,-1) << ") polar\n" // atan2(1, -1) = +3pi/4, Quad II
              << "(-1,-1) cartesian is (" << hypot(-1,-1)
              << ',' << atan2(-1,-1) << ") polar\n" // atan2(-1,-1) = -3pi/4, Quad III
              << "(-1,1) cartesian is (" << hypot(-1,1)
              << ',' << 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';
}

(+1,+1) cartesian is (1.41421,0.785398) polar
(+1,-1) cartesian is (1.41421,2.35619) polar
(-1,-1) cartesian is (1.41421,-2.35619) polar
(-1,1) cartesian is (1.41421,-0.785398) polar
atan2(0, 0) = 0 atan2(0,-0) = 3.14159
atan2(7, 0) = 1.5708 atan2(7,-0) = 1.5708

See also