|
111
|
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 -- --
|
|
145
|
9 -- Copyright (C) 1992-2019, Free Software Foundation, Inc. --
|
|
111
|
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
|
|
|
32 package 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
|
|
|
79 end System.Exp_Mod;
|
