atan2

auto eve::atan2 = functor<atan2_t>

inlineconstexpr

Header file

#include <eve/module/core.hpp>

Callable Signatures

Header file

#include <eve/module/core.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto atan2(floating_value auto x, floating_value auto y)                          noexcept; // 1
 
   // Semantic option
   constexpr auto atan2[rad](floating_value auto x, floating_value auto y)                     noexcept; // 1.a
   constexpr auto atan2[deg](floating_value auto x, floating_value auto y)                     noexcept; // 1.b
   constexpr auto atan2[pirad](floating_value auto x, floating_value auto y)                   noexcept; // 1.c
   constexpr auto atan2[pedantic](floating_value auto x, floating_value auto y)                noexcept; // 2
 
   // Lanes masking
   constexpr auto atan2[conditional_expr auto c][floating_value auto x, floating_value auto y) noexcept; // 3
   constexpr auto atan2[logical_value auto m](floating_value auto x, floating_value auto y)    noexcept; // 3
}

Parameters

• x, y: floating values.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. The arc tangent of \(\frac{y}x\) in the radian range \([-\pi , +\pi]\) (1.a) , is returned. (converted in degrees (1.b) or in \([\pi\) multiples (1.c)) For 1.a The IEEE limiting values are almost all satisfied :
   • If x and y are both zero or infinites, Nan is returned (this is not standard conforming)
   • If y is \(\pm0\) and x is strictly negative or \(-0\), \(\pm\pi\) is returned
   • If y is \(\pm0\) and x is strictly positive or \(+0\), \(\pm0\) is returned
   • If y is \(\pm\infty\) and x is finite, \(\pm\frac\pi2\) is returned
   • If x is \(\pm0\) and y is strictly negative, \(-\frac\pi2\) is returned
   • If x is \(\pm0\) and y is strictly positive, \(+\frac\pi2\) is returned
   • If x is \(-\infty\) and y is finite and positive, \(+\pi\) is returned
   • If x is \(-\infty\) and y is finite and negative, \(-\pi\) is returned
   • If x is \(+\infty\) and y is finite and positive, \(+0\) is returned
   • If x is \(+\infty\) and y is finite and negative, \(-0\) is returned
   • If either x is Nan or y is Nan, Nan is returned

The call will return a NaN if x and y are both either null or infinite: this result is not IEEE conformant, but allows to simplify (and speed up) the implementation. In all other cases, the result is standard conformant. And the converted equivalent are returned with the other units.

1. Same as 1, except that all IEEE limiting values are satisfied :
   • If y is \(\pm\infty\) and x is \(-\infty\), \(\pm\frac{3\pi}4\) is returned
   • If y is \(\pm\infty\) and x is \(+\infty\), \(\pm\frac{\pi}4\) is returned
   • If x is \(\pm0\) and y is \(\pm-0\), \(-\frac\pi2\) is returned
   • If x is \(\pm0\) and y is \(\pm+0\), \(+\frac\pi2\) is returned
2. The operation is performed conditionnaly.

External references

• C++ standard reference:atan2
• Wolfram MathWorld: Inverse Tangent
• Wikipedia: Atan2

Example

// revision 1
#include <eve/module/math.hpp>
#include <iostream>
 
int main()
{
  eve::wide pf = { 0.0f, 1.0f, 4.0f, -2.0f, eve::inf(eve::as<float>()), 0.0f, eve::minf(eve::as<float>()), 1.0f};
  eve::wide qf = { 1.0f, -1.0f, 3.0f, -0.0f, 1.0f, 0.0f, 0.0f, -0.0f};
 
  std::cout << "<- pf                           = " << pf << "\n";
  std::cout << "<- qf                           = " << qf << "\n";
 
  std::cout << "-> atan2(pf, qf)                = " << eve::atan2(pf, qf) << "\n";
  std::cout << "-> atan2[deg](pf, qf)           = " << eve::atan2[eve::deg](pf, qf) << "\n";
  std::cout << "-> atan2[radpi](pf, qf)         = " << eve::atan2[eve::radpi](pf, qf) << "\n";
  std::cout << "-> atan2[rad](pf, qf)           = " << eve::atan2[eve::rad](pf, qf) << "\n";
  std::cout << "-> atan2[pedantic](pf, qf)      = " << eve::atan2[eve::pedantic](pf, qf) << "\n";
  std::cout << "-> atan2[ignore_last(2)](pf, qf)= " << eve::atan2[eve::ignore_last(2)](pf, qf) << "\n";
  std::cout << "-> atan2[pf != -2.0f](pf, qf)   = " << eve::atan2[pf != -2.0f](pf, qf) << "\n";
}