| ------------------------------------------------------------------------------ |
| -- -- |
| -- 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; |
