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+
+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;
+