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# std::atan2

From cppreference.com
< cpp‎ | numeric‎ | math

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

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.

### [edit] Parameters

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

### [edit] 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.

### [edit] 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 negative 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

### [edit] 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.

### [edit] Example

Run this code

    #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';
    }

Output:

    (+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

### [edit] See also

asin | computes arc sine (arcsin(x)) (function) [edit]
acos | computes arc cosine (arccos(x)) (function) [edit]
atan | computes arc tangent (arctan(x)) (function) [edit]
arg | returns the phase angle (function template) [edit]
atan2(std::valarray) | applies the function std::atan2 to a valarray and a value (function template) [edit]
C documentation for atan2

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