| ------------------------------------------------------------------------------ |
| -- -- |
| -- GNAT RUN-TIME COMPONENTS -- |
| -- -- |
| -- S Y S T E M . E X P _ M O D -- |
| -- -- |
| -- B o d y -- |
| -- -- |
| -- Copyright (C) 1992-2021, 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. -- |
| -- -- |
| ------------------------------------------------------------------------------ |
| |
| package body System.Exp_Mod is |
| use System.Unsigned_Types; |
| |
| ----------------- |
| -- Exp_Modular -- |
| ----------------- |
| |
| function Exp_Modular |
| (Left : Unsigned; |
| Modulus : Unsigned; |
| Right : Natural) return Unsigned |
| is |
| Result : Unsigned := 1; |
| Factor : Unsigned := Left; |
| Exp : Natural := Right; |
| |
| function Mult (X, Y : Unsigned) return Unsigned is |
| (Unsigned (Long_Long_Unsigned (X) * Long_Long_Unsigned (Y) |
| mod Long_Long_Unsigned (Modulus))); |
| -- Modular multiplication. Note that we can't take advantage of the |
| -- compiler's circuit, because the modulus is not known statically. |
| |
| 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 the cases of 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 |
| if Exp rem 2 /= 0 then |
| Result := Mult (Result, Factor); |
| end if; |
| |
| Exp := Exp / 2; |
| exit when Exp = 0; |
| Factor := Mult (Factor, Factor); |
| end loop; |
| end if; |
| |
| return Result; |
| |
| end Exp_Modular; |
| |
| end System.Exp_Mod; |
