std::atan2(std::valarray)

Header: <valarray>

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

# Declarations

template< class T >
std::valarray<T> atan2( const std::valarray<T>& y, const std::valarray<T>& x );

template< class T >
std::valarray<T> atan2( const std::valarray<T>& y,
const typename std::valarray<T>::value_type& vx );

template< class T >
std::valarray<T> atan2( const typename std::valarray<T>::value_type& vy,
const std::valarray<T>& 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:

# Example

#include <algorithm>
#include <cmath>
#include <iomanip>
#include <iostream>
#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));
}

# Defect reports

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