generic
    type Real is delta <> digits <>;
package Complex_Fixed_Points is

    pragma Pure (Complex_Fixed_Points);

    type Complex is private;
    type Imaginary is private;
    pragma Preelaborable_Initialization (Imaginary);

    i : constant Imaginary;
    j : constant Imaginary;

    Zero : constant Complex;
    One  : constant Complex;

    function Re (X : in Complex) return Real'Base;
    function Im (X : in Complex) return Real'Base;
    function Im (X : in Imaginary) return Real'Base;

    procedure Set_Re
           (X  : in out Complex;
            Re : in     Real'Base);
    procedure Set_Im
           (X  : in out Complex;
            Im : in     Real'Base);
    procedure Set_Im
           (X  : in out Imaginary;
            Im : in     Real'Base);

    function Cartesian (Re, Im : in Real'Base) return Complex;
    function Cartesian (Re     : in Real'Base) return Complex;
    function Cartesian (Im     : in Imaginary) return Complex;

    function Modulus (X     : in Complex) return Real'Base;
    function "abs"   (Right : in Complex) return Real'Base renames Modulus;

    --  Like hell am I writing fixed point trig functions right now.

    --  function Argument (X : in Complex) return Real'Base;
    --  function Argument (X : in Complex; Cycle : in Real'Base) return Real'Base;

    --  function Polar (Modulus, Argument        : in Real'Base) return Complex;
    --  function Polar (Modulus, Argument, Cycle : in Real'Base) return Complex;

    function "+" (Right : in Complex) return Complex;
    function "-" (Right : in Complex) return Complex;
    function Conjugate (X : in Complex) return Complex;

    function "+" (Left, Right : in Complex) return Complex;
    function "-" (Left, Right : in Complex) return Complex;
    function "*" (Left, Right : in Complex) return Complex;
    function "/" (Left, Right : in Complex) return Complex;

    function "**" (Left : in Complex; Right : in Integer) return Complex;

    function "+"       (Right : in Imaginary) return Imaginary;
    function "-"       (Right : in Imaginary) return Imaginary;
    function Conjugate (X     : in Imaginary) return Imaginary renames "-";
    function "abs"     (Right : in Imaginary) return Real'Base;

    function "+" (Left, Right : in Imaginary) return Imaginary;
    function "-" (Left, Right : in Imaginary) return Imaginary;
    function "*" (Left, Right : in Imaginary) return Real'Base;
    function "/" (Left, Right : in Imaginary) return Real'Base;

    function "**" (Left : in Imaginary; Right : in Integer) return Complex;

    function "<"  (Left, Right : in Imaginary) return Boolean;
    function "<=" (Left, Right : in Imaginary) return Boolean;
    function ">"  (Left, Right : in Imaginary) return Boolean;
    function ">=" (Left, Right : in Imaginary) return Boolean;

    function "+" (Left : in Complex;   Right : in Real'Base) return Complex;
    function "+" (Left : in Real'Base; Right : in Complex)   return Complex;
    function "-" (Left : in Complex;   Right : in Real'Base) return Complex;
    function "-" (Left : in Real'Base; Right : in Complex)   return Complex;
    function "*" (Left : in Complex;   Right : in Real'Base) return Complex;
    function "*" (Left : in Real'Base; Right : in Complex)   return Complex;
    function "/" (Left : in Complex;   Right : in Real'Base) return Complex;
    function "/" (Left : in Real'Base; Right : in Complex)   return Complex;

    function "+" (Left : in Complex;   Right : in Imaginary) return Complex;
    function "+" (Left : in Imaginary; Right : in Complex)   return Complex;
    function "-" (Left : in Complex;   Right : in Imaginary) return Complex;
    function "-" (Left : in Imaginary; Right : in Complex)   return Complex;
    function "*" (Left : in Complex;   Right : in Imaginary) return Complex;
    function "*" (Left : in Imaginary; Right : in Complex)   return Complex;
    function "/" (Left : in Complex;   Right : in Imaginary) return Complex;
    function "/" (Left : in Imaginary; Right : in Complex)   return Complex;

    function "+" (Left : in Imaginary; Right : in Real'Base) return Complex;
    function "+" (Left : in Real'Base; Right : in Imaginary) return Complex;
    function "-" (Left : in Imaginary; Right : in Real'Base) return Complex;
    function "-" (Left : in Real'Base; Right : in Imaginary) return Complex;
    function "*" (Left : in Imaginary; Right : in Real'Base) return Imaginary;
    function "*" (Left : in Real'Base; Right : in Imaginary) return Imaginary;
    function "/" (Left : in Imaginary; Right : in Real'Base) return Imaginary;
    function "/" (Left : in Real'Base; Right : in Imaginary) return Imaginary;

private

    type Complex is record
        Re, Im : Real'Base;
    end record;

    type Imaginary is new Real'Base;

    i : constant Imaginary := 1.0;
    j : constant Imaginary := 1.0;

    Zero : constant Complex := (Re => 0.0, Im => 0.0);
    One  : constant Complex := (Re => 1.0, Im => 0.0);

end Complex_Fixed_Points;