1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
|
------------------------------------------------------------------------------
-- --
-- GNAT RUN-TIME COMPONENTS --
-- --
-- S Y S T E M . E X P _ M O D --
-- --
-- B o d y --
-- --
-- Copyright (C) 1992-2009 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
-----------------
-- Exp_Modular --
-----------------
function Exp_Modular
(Left : Integer;
Modulus : Integer;
Right : Natural)
return Integer
is
Result : Integer := 1;
Factor : Integer := Left;
Exp : Natural := Right;
function Mult (X, Y : Integer) return Integer;
pragma Inline (Mult);
-- Modular multiplication. Note that we can't take advantage of the
-- compiler's circuit, because the modulus is not known statically.
function Mult (X, Y : Integer) return Integer is
begin
return Integer
(Long_Long_Integer (X) * Long_Long_Integer (Y)
mod Long_Long_Integer (Modulus));
end Mult;
-- Start of processing for Exp_Modular
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;
|
