------------------------------------------------------------------------------
--                                                                          --
--                         GNAT RUN-TIME COMPONENTS                         --
--                                                                          --
--                        S Y S T E M . E X P O N U                         --
--                                                                          --
--                                 B o d y                                  --
--                                                                          --
--          Copyright (C) 1992-2022, Free Software Foundation, Inc.         --
--                                                                          --
-- 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- --
-- ware  Foundation;  either version 3,  or (at your option) any later ver- --
-- sion.  GNAT is distributed in the hope that it will be useful, but WITH- --
-- OUT ANY WARRANTY;  without even the  implied warranty of MERCHANTABILITY --
-- or FITNESS FOR A PARTICULAR PURPOSE.                                     --
--                                                                          --
-- As a special exception under Section 7 of GPL version 3, you are granted --
-- additional permissions described in the GCC Runtime Library Exception,   --
-- version 3.1, as published by the Free Software Foundation.               --
--                                                                          --
-- You should have received a copy of the GNU General Public License and    --
-- a copy of the GCC Runtime Library Exception along with this program;     --
-- see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see    --
-- <http://www.gnu.org/licenses/>.                                          --
--                                                                          --
-- GNAT was originally developed  by the GNAT team at  New York University. --
-- Extensive contributions were provided by Ada Core Technologies Inc.      --
--                                                                          --
------------------------------------------------------------------------------

function System.Exponu (Left : Int; Right : Natural) return Int
  with SPARK_Mode
is
   --  Preconditions, postconditions, ghost code, loop invariants and
   --  assertions in this unit are meant for analysis only, not for run-time
   --  checking, as it would be too costly otherwise. This is enforced by
   --  setting the assertion policy to Ignore.

   pragma Assertion_Policy (Pre            => Ignore,
                            Post           => Ignore,
                            Ghost          => Ignore,
                            Loop_Invariant => Ignore,
                            Assert         => Ignore);

   --  Note that negative exponents get a constraint error because the
   --  subtype of the Right argument (the exponent) is Natural.

   Result : Int     := 1;
   Factor : Int     := Left;
   Exp    : Natural := Right;

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 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
         pragma Loop_Invariant (Exp > 0);
         pragma Loop_Invariant (Result * Factor ** Exp = Left ** Right);
         pragma Loop_Variant (Decreases => Exp);

         if Exp rem 2 /= 0 then
            pragma Assert
              (Result * (Factor * Factor ** (Exp - 1)) = Left ** Right);
            pragma Assert
              ((Result * Factor) * Factor ** (Exp - 1) = Left ** Right);

            Result := Result * Factor;
         end if;

         Exp := Exp / 2;
         exit when Exp = 0;
         Factor := Factor * Factor;
      end loop;
   end if;

   return Result;
end System.Exponu;