1------------------------------------------------------------------------------
2--                                                                          --
3--                         GNAT RUN-TIME COMPONENTS                         --
4--                                                                          --
5--                       S Y S T E M . E X P _ M O D                        --
6--                                                                          --
7--                                 B o d y                                  --
8--                                                                          --
9--          Copyright (C) 1992-2014, Free Software Foundation, Inc.         --
10--                                                                          --
11-- GNAT is free software;  you can  redistribute it  and/or modify it under --
12-- terms of the  GNU General Public License as published  by the Free Soft- --
13-- ware  Foundation;  either version 3,  or (at your option) any later ver- --
14-- sion.  GNAT is distributed in the hope that it will be useful, but WITH- --
15-- OUT ANY WARRANTY;  without even the  implied warranty of MERCHANTABILITY --
16-- or FITNESS FOR A PARTICULAR PURPOSE.                                     --
17--                                                                          --
18-- As a special exception under Section 7 of GPL version 3, you are granted --
19-- additional permissions described in the GCC Runtime Library Exception,   --
20-- version 3.1, as published by the Free Software Foundation.               --
21--                                                                          --
22-- You should have received a copy of the GNU General Public License and    --
23-- a copy of the GCC Runtime Library Exception along with this program;     --
24-- see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see    --
25-- <http://www.gnu.org/licenses/>.                                          --
26--                                                                          --
27-- GNAT was originally developed  by the GNAT team at  New York University. --
28-- Extensive contributions were provided by Ada Core Technologies Inc.      --
29--                                                                          --
30------------------------------------------------------------------------------
31
32package body System.Exp_Mod is
33   use System.Unsigned_Types;
34
35   -----------------
36   -- Exp_Modular --
37   -----------------
38
39   function Exp_Modular
40     (Left    : Unsigned;
41      Modulus : Unsigned;
42      Right   : Natural) return Unsigned
43   is
44      Result : Unsigned := 1;
45      Factor : Unsigned := Left;
46      Exp    : Natural := Right;
47
48      function Mult (X, Y : Unsigned) return Unsigned is
49        (Unsigned (Long_Long_Unsigned (X) * Long_Long_Unsigned (Y)
50                    mod Long_Long_Unsigned (Modulus)));
51      --  Modular multiplication. Note that we can't take advantage of the
52      --  compiler's circuit, because the modulus is not known statically.
53
54   begin
55      --  We use the standard logarithmic approach, Exp gets shifted right
56      --  testing successive low order bits and Factor is the value of the
57      --  base raised to the next power of 2.
58
59      --  Note: it is not worth special casing the cases of base values -1,0,+1
60      --  since the expander does this when the base is a literal, and other
61      --  cases will be extremely rare.
62
63      if Exp /= 0 then
64         loop
65            if Exp rem 2 /= 0 then
66               Result := Mult (Result, Factor);
67            end if;
68
69            Exp := Exp / 2;
70            exit when Exp = 0;
71            Factor := Mult (Factor, Factor);
72         end loop;
73      end if;
74
75      return Result;
76
77   end Exp_Modular;
78
79end System.Exp_Mod;
80