------------------------------------------------------------------------------
--                                                                          --
--                         GNAT RUN-TIME COMPONENTS                         --
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--                       S Y S T E M . E X P _ M O D                        --
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--          Copyright (C) 1992-2018, Free Software Foundation, Inc.         --
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-- GNAT is free software;  you can  redistribute it  and/or modify it under --
-- terms of the  GNU General Public License as published  by the Free Soft- --
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-- GNAT was originally developed  by the GNAT team at  New York University. --
-- Extensive contributions were provided by Ada Core Technologies Inc.      --
--                                                                          --
------------------------------------------------------------------------------

package body System.Exp_Mod is
   use System.Unsigned_Types;

   -----------------
   -- Exp_Modular --
   -----------------

   function Exp_Modular
     (Left    : Unsigned;
      Modulus : Unsigned;
      Right   : Natural) return Unsigned
   is
      Result : Unsigned := 1;
      Factor : Unsigned := Left;
      Exp    : Natural := Right;

      function Mult (X, Y : Unsigned) return Unsigned is
        (Unsigned (Long_Long_Unsigned (X) * Long_Long_Unsigned (Y)
                    mod Long_Long_Unsigned (Modulus)));
      --  Modular multiplication. Note that we can't take advantage of the
      --  compiler's circuit, because the modulus is not known statically.

   begin
      --  We use the standard logarithmic approach, Exp gets shifted right
      --  testing successive low order bits and Factor is the value of the
      --  base raised to the next power of 2.

      --  Note: it is not worth special casing the cases of base values -1,0,+1
      --  since the expander does this when the base is a literal, and other
      --  cases will be extremely rare.

      if Exp /= 0 then
         loop
            if Exp rem 2 /= 0 then
               Result := Mult (Result, Factor);
            end if;

            Exp := Exp / 2;
            exit when Exp = 0;
            Factor := Mult (Factor, Factor);
         end loop;
      end if;

      return Result;

   end Exp_Modular;

end System.Exp_Mod;