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This language feature is available from Ada 95 on. Ada.Numerics.Generic_Complex_Types is a unit of the Predefined Language Environment since Ada 95.

The generic package Ada.Numerics.Generic_Complex_Types defines complex type for a defined floating point type. Being generic it can not only be used for predefined floating point types but also for any user defined floating type.

Usage

There is an extensive usage guide in Ada Programming/Mathematical calculations. Here the relevant extract:

with Ada.Numerics.Generic_Complex_Types;

procedure Numeric_7 is

  type Value_Type is digits 12 range
     -999_999_999_999.0e999 .. 999_999_999_999.0e999;

  package Complex_Types is new Ada.Numerics.Generic_Complex_Types (
     Value_Type);

  use type Complex_Types.Complex;

Specification

--                     Standard Ada library specification
--   Copyright (c) 2003-2018 Maxim Reznik <reznikmm@gmail.com>
--   Copyright (c) 2004-2016 AXE Consultants
--   Copyright (c) 2004, 2005, 2006 Ada-Europe
--   Copyright (c) 2000 The MITRE Corporation, Inc.
--   Copyright (c) 1992, 1993, 1994, 1995 Intermetrics, Inc.
--   SPDX-License-Identifier: BSD-3-Clause and LicenseRef-AdaReferenceManual
-- -------------------------------------------------------------------------

generic
   type Real is digits <>;
package Ada.Numerics.Generic_Complex_Types is
   pragma Pure (Generic_Complex_Types);

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

   type Imaginary is private;
   pragma Preelaborable_Initialization (Imaginary);

   i : constant Imaginary;
   j : constant Imaginary;

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

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

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

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

   function Compose_From_Polar (Modulus, Argument        : Real'Base)
                               return Complex;
   function Compose_From_Polar (Modulus, Argument, Cycle : Real'Base)
                               return Complex;

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

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

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

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

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

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

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

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

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

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

private

   type Imaginary is new Real'Base;
   i : constant Imaginary := 1.0;
   j : constant Imaginary := 1.0;

end Ada.Numerics.Generic_Complex_Types;

See also