gcc/ada/s-expmod.adb

   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
  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;