# std::atan2(std::valarray)

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< cpp‎ | numeric‎ | valarray

Defined in header `<valarray>` |  |
template< class T > std::valarray<T> atan2( const std::valarray<T>& y, const std::valarray<T>& x ); | (1) |
template< class T > std::valarray<T> atan2( const std::valarray<T>& y, const typename std::valarray<T>::value_type& vx ); | (2) |
template< class T > std::valarray<T> atan2( const typename std::valarray<T>::value_type& vy, const std::valarray<T>& x ); | (3) |

Computes the inverse tangent of `y/x` using the signs of arguments to correctly determine quadrant.

1) Computes the inverse tangent of each pair of corresponding values from `y` and `x`.

The behavior is undefined if x.size() != y.size().

2) Computes the inverse tangent of `vx` and each value in the numeric array `y`.
3) Computes the inverse tangent of `vy` and each value in the numeric array `x`.

### Parameters

x, y | - | numeric arrays to compute inverse tangent of
vy, vx | - | values to compute inverse tangent of

### Return value

A numeric array containing the results of computation of inverse tangent.

### Notes

Unqualified function (atan2) is used to perform the computation. If such function is not available, std::atan2 is used due to argument-dependent lookup.

The function can be implemented with the return type different from std::valarray. In this case, the replacement type has the following properties:

  - All const member functions of std::valarray are provided.
  - std::valarray, std::slice_array, std::gslice_array, std::mask_array and std::indirect_array can be constructed from the replacement type.
  - All functions accepting an argument of type const std::valarray& except `begin()` and `end()` (since C++11) should also accept the replacement type.
  - All functions accepting two arguments of type const std::valarray& should accept every combination of const std::valarray& and the replacement type.
  - The return type does not add more than two levels of template nesting over the most deeply-nested argument type.

### Example

Run this code

    #include <algorithm>
    #include <cmath>
    #include <iostream>
    #include <iomanip>
    #include <valarray>

    void show(char const* title, const std::valarray<double>& va) {
        std::cout << title << " ";
        std::for_each(std::begin(va), std::end(va), [](const double x) {
            std::cout << " " << std::right << std::setw(4) << x << "°";
        });
        std::cout << '\n';
    }

    const double pi = std::acos(-1.0); // C++20: std::numbers::pi

    int main()
    {
        auto degrees_to_radians = [](double const& x) { return (pi * x / 180); };
        auto radians_to_degrees = [](double const& x) { return (180 * x / pi); };

        const std::valarray<double> degrees{-90, -60, -45, -30, 0, 30, 45, 60, 90};
        const std::valarray<double> radians = degrees.apply(degrees_to_radians);

        const auto sin = std::sin(radians);
        const auto cos = std::cos(radians);

        show("(1)", std::atan2(sin, cos).apply(radians_to_degrees));
        show("(2)", std::atan2(sin/cos, 1.0).apply(radians_to_degrees));
        show("(3)", std::atan2(1.0, cos/sin).apply(radians_to_degrees));
    }

Output:

    (1)   -90°  -60°  -45°  -30°    0°   30°   45°   60°   90°
    (2)   -90°  -60°  -45°  -30°    0°   30°   45°   60°   90°
    (3)    90°  120°  135°  150°    0°   30°   45°   60°   90°

### Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR | Applied to | Behavior as published | Correct behavior
--- | --- | --- | ---
LWG 3074 | C++98 | `T` is deduced from both the scalar and the `valarray` for (2-3), disallowing mixed-type calls | only deduce `T` from the `valarray`

### See also

asin(std::valarray) | applies the function std::asin to each element of valarray (function template)
acos(std::valarray) | applies the function std::acos to each element of valarray (function template)
atan(std::valarray) | applies the function std::atan to each element of valarray (function template)
atan2 atan2f atan2l (C++11)(C++11) | arc tangent, using signs to determine quadrants (function)
arg | returns the phase angle (function template)

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