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### 8.22 `ATAN2` — Arctangent function

Description:
  `ATAN2(Y, X)` computes the principal value of the argument function of the complex number X + i Y. This function can be used to transform from Cartesian into polar coordinates and allows to determine the angle in the correct quadrant.
Standard:
  Fortran 77 and later
Class:
  Elemental function
Syntax:
  `RESULT = ATAN2(Y, X)`
Arguments:

  Y | The type shall be `REAL`.
  X | The type and kind type parameter shall be the same as Y. If Y is zero, then X must be nonzero.

Return value:
  The return value has the same type and kind type parameter as Y. It is the principal value of the complex number X + i Y. If X is nonzero, then it lies in the range -\pi \le \atan (x) \leq \pi. The sign is positive if Y is positive. If Y is zero, then the return value is zero if X is strictly positive, \pi if X is negative and Y is positive zero (or the processor does not handle signed zeros), and -\pi if X is negative and Y is negative zero. Finally, if X is zero, then the magnitude of the result is \pi/2.
Example:

                program test_atan2
                  real(4) :: x = 1.e0_4, y = 0.5e0_4
                  x = atan2(y,x)
                end program test_atan2

Specific names:

  Name | Argument | Return type | Standard
  `ATAN2(X, Y)` | `REAL(4) X, Y` | `REAL(4)` | Fortran 77 and later
  `DATAN2(X, Y)` | `REAL(8) X, Y` | `REAL(8)` | Fortran 77 and later