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------------------------------------------------------------------------------
-- --
-- GNAT RUN-TIME COMPONENTS --
-- --
-- S Y S T E M . E X P O N U --
-- --
-- B o d y --
-- --
-- Copyright (C) 1992-2024, 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;
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