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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 positive and \pi if X is negative. 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