------------------------------------------------------------------------------
-- --
-- GNAT RUN-TIME COMPONENTS --
-- --
-- S Y S T E M . E X P _ M O D --
-- --
-- S p e c --
-- --
-- Copyright (C) 1992-2023, 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. --
-- --
------------------------------------------------------------------------------
-- This function performs exponentiation of a modular type with nonbinary
-- modulus values. Arithmetic is done in Long_Long_Unsigned, with explicit
-- accounting for the modulus value which is passed as the second argument.
-- Note that 1 is a binary modulus (2**0), so the compiler should not (and
-- will not) call this function with Modulus equal to 1.
-- Preconditions in this unit are meant for analysis only, not for run-time
-- checking, so that the expected exceptions are raised. This is enforced by
-- setting the corresponding assertion policy to Ignore. Postconditions and
-- contract cases should not be executed at runtime as well, in order not to
-- slow down the execution of these functions.
pragma Assertion_Policy (Pre => Ignore,
Post => Ignore,
Contract_Cases => Ignore,
Ghost => Ignore);
with Ada.Numerics.Big_Numbers.Big_Integers_Ghost;
with System.Unsigned_Types;
package System.Exp_Mod
with Pure, SPARK_Mode
is
use type System.Unsigned_Types.Unsigned;
subtype Unsigned is System.Unsigned_Types.Unsigned;
use type Ada.Numerics.Big_Numbers.Big_Integers_Ghost.Big_Integer;
subtype Big_Integer is
Ada.Numerics.Big_Numbers.Big_Integers_Ghost.Big_Integer
with Ghost;
package Unsigned_Conversion is
new Ada.Numerics.Big_Numbers.Big_Integers_Ghost.Unsigned_Conversions
(Int => Unsigned);
function Big (Arg : Unsigned) return Big_Integer is
(Unsigned_Conversion.To_Big_Integer (Arg))
with Ghost;
subtype Power_Of_2 is Unsigned with
Dynamic_Predicate =>
Power_Of_2 /= 0 and then (Power_Of_2 and (Power_Of_2 - 1)) = 0;
function Exp_Modular
(Left : Unsigned;
Modulus : Unsigned;
Right : Natural) return Unsigned
with
Pre => Modulus /= 0 and then Modulus not in Power_Of_2,
Post => Big (Exp_Modular'Result) = Big (Left) ** Right mod Big (Modulus);
end System.Exp_Mod;