| ------------------------------------------------------------------------------ |
| -- -- |
| -- GNAT RUN-TIME COMPONENTS -- |
| -- -- |
| -- S Y S T E M . E X P _ M O D -- |
| -- -- |
| -- S p e c -- |
| -- -- |
| -- 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. -- |
| -- -- |
| ------------------------------------------------------------------------------ |
| |
| -- 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; |
