------------------------------------------------------------------------------
--                                                                          --
--                         GNAT RUN-TIME COMPONENTS                         --
--                                                                          --
--                  ADA.NUMERICS.BIG_NUMBERS.BIG_INTEGERS                   --
--                                                                          --
--                                 S p e c                                  --
--                                                                          --
-- This specification is derived from the Ada Reference Manual for use with --
-- GNAT.  In accordance with the copyright of that document, you can freely --
-- copy and modify this specification,  provided that if you redistribute a --
-- modified version,  any changes that you have made are clearly indicated. --
--                                                                          --
------------------------------------------------------------------------------

package Ada.Numerics.Big_Numbers.Big_Integers with
   SPARK_Mode,
   Ghost,
   Preelaborate
is
   type Big_Integer is private
     with Integer_Literal => From_Universal_Image;

   function Is_Valid (Arg : Big_Integer) return Boolean
   with
     Import,
     Global => null;

   subtype Valid_Big_Integer is Big_Integer
     with Dynamic_Predicate => Is_Valid (Valid_Big_Integer),
          Predicate_Failure => raise Program_Error;

   function "=" (L, R : Valid_Big_Integer) return Boolean with
      Import,
      Global => null;

   function "<" (L, R : Valid_Big_Integer) return Boolean with
      Import,
      Global => null;

   function "<=" (L, R : Valid_Big_Integer) return Boolean with
      Import,
      Global => null;

   function ">" (L, R : Valid_Big_Integer) return Boolean with
      Import,
      Global => null;

   function ">=" (L, R : Valid_Big_Integer) return Boolean with
      Import,
      Global => null;

   function To_Big_Integer (Arg : Integer) return Valid_Big_Integer
     with
       Import,
       Global => null;

   subtype Big_Positive is Big_Integer
     with Dynamic_Predicate =>
            (if Is_Valid (Big_Positive)
             then Big_Positive > To_Big_Integer (0)),
          Predicate_Failure => (raise Constraint_Error);

   subtype Big_Natural is Big_Integer
     with Dynamic_Predicate =>
            (if Is_Valid (Big_Natural)
             then Big_Natural >= To_Big_Integer (0)),
          Predicate_Failure => (raise Constraint_Error);

   function In_Range
     (Arg : Valid_Big_Integer; Low, High : Big_Integer) return Boolean
   is (Low <= Arg and Arg <= High)
   with
     Import,
     Global => null;

   function To_Integer (Arg : Valid_Big_Integer) return Integer
   with
     Import,
     Pre    => In_Range (Arg,
                         Low  => To_Big_Integer (Integer'First),
                         High => To_Big_Integer (Integer'Last))
                or else (raise Constraint_Error),
     Global => null;

   generic
      type Int is range <>;
   package Signed_Conversions is

      function To_Big_Integer (Arg : Int) return Valid_Big_Integer
      with
        Global => null;

      function From_Big_Integer (Arg : Valid_Big_Integer) return Int
      with
        Pre    => In_Range (Arg,
                            Low  => To_Big_Integer (Int'First),
                            High => To_Big_Integer (Int'Last))
                   or else (raise Constraint_Error),
        Global => null;
   end Signed_Conversions;

   generic
      type Int is mod <>;
   package Unsigned_Conversions is

      function To_Big_Integer (Arg : Int) return Valid_Big_Integer
      with
        Global => null;

      function From_Big_Integer (Arg : Valid_Big_Integer) return Int
      with
        Pre    => In_Range (Arg,
                            Low  => To_Big_Integer (Int'First),
                            High => To_Big_Integer (Int'Last))
                   or else (raise Constraint_Error),
        Global => null;

   end Unsigned_Conversions;

   function From_String (Arg : String) return Valid_Big_Integer
   with
     Import,
     Global => null;

   function From_Universal_Image (Arg : String) return Valid_Big_Integer
     renames From_String;

   function "+" (L : Valid_Big_Integer) return Valid_Big_Integer
   with
     Import,
     Global => null;

   function "-" (L : Valid_Big_Integer) return Valid_Big_Integer
   with
     Import,
     Global => null;

   function "abs" (L : Valid_Big_Integer) return Valid_Big_Integer
   with
     Import,
     Global => null;

   function "+" (L, R : Valid_Big_Integer) return Valid_Big_Integer
   with
     Import,
     Global => null;

   function "-" (L, R : Valid_Big_Integer) return Valid_Big_Integer
   with
     Import,
     Global => null;

   function "*" (L, R : Valid_Big_Integer) return Valid_Big_Integer
   with
     Import,
     Global => null;

   function "/" (L, R : Valid_Big_Integer) return Valid_Big_Integer
   with
     Import,
     Global => null;

   function "mod" (L, R : Valid_Big_Integer) return Valid_Big_Integer
   with
     Import,
     Global => null;

   function "rem" (L, R : Valid_Big_Integer) return Valid_Big_Integer
   with
     Import,
     Global => null;

   function "**" (L : Valid_Big_Integer; R : Natural) return Valid_Big_Integer
   with
     Import,
     Global => null;

   function Min (L, R : Valid_Big_Integer) return Valid_Big_Integer
   with
     Import,
     Global => null;

   function Max (L, R : Valid_Big_Integer) return Valid_Big_Integer
   with
     Import,
     Global => null;

   function Greatest_Common_Divisor
     (L, R : Valid_Big_Integer) return Big_Positive
   with
     Import,
     Pre    => (L /= To_Big_Integer (0) and R /= To_Big_Integer (0))
             or else (raise Constraint_Error),
     Global => null;

private
   pragma SPARK_Mode (Off);

   type Big_Integer is null record;

end Ada.Numerics.Big_Numbers.Big_Integers;