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------------------------------------------------------------------------------

--                                                                          --

--                         GNAT RUN-TIME COMPONENTS                         --

--                                                                          --

--         A D A . N U M E R I C S . D I S C R E T E _ R A N D O M          --

--                                                                          --

--                                 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.      --

--                                                                          --

------------------------------------------------------------------------------

with Ada.Calendar;

with Interfaces; use Interfaces;

package body Ada.Numerics.Discrete_Random is

   -------------------------

   -- Implementation Note --

   -------------------------

   --  The design of this spec is very awkward, as a result of Ada 95 not

   --  permitting in-out parameters for function formals (most naturally

   --  Generator values would be passed this way). In pure Ada 95, the only

   --  solution is to use the heap and pointers, and, to avoid memory leaks,

   --  controlled types.

   --  This is awfully heavy, so what we do is to use Unrestricted_Access to

   --  get a pointer to the state in the passed Generator. This works because

   --  Generator is a limited type and will thus always be passed by reference.

   type Pointer is access all State;

   Fits_In_32_Bits : constant Boolean :=

                       Rst'Size < 31

                         or else (Rst'Size = 31

                                  and then Rst'Pos (Rst'First) < 0);

   --  This is set True if we do not need more than 32 bits in the result. If

   --  we need 64-bits, we will only use the meaningful 48 bits of any 64-bit

   --  number generated, since if more than 48 bits are required, we split the

   --  computation into two separate parts, since the algorithm does not behave

   --  above 48 bits.

   --  The way this expression works is that obviously if the size is 31 bits,

   --  it fits in 32 bits. In the 32-bit case, it fits in 32-bit signed if the

   --  range has negative values. It is too conservative in the case that the

   --  programmer has set a size greater than the default, e.g. a size of 33

   --  for an integer type with a range of 1..10, but an over-conservative

   --  result is OK. The important thing is that the value is only True if

   --  we know the result will fit in 32-bits signed. If the value is False

   --  when it could be True, the behavior will be correct, just a bit less

   --  efficient than it could have been in some unusual cases.

   --

   --  One might assume that we could get a more accurate result by testing

   --  the lower and upper bounds of the type Rst against the bounds of 32-bit

   --  Integer. However, there is no easy way to do that. Why? Because in the

   --  relatively rare case where this expresion has to be evaluated at run

   --  time rather than compile time (when the bounds are dynamic), we need a

   --  type to use for the computation. But the possible range of upper bound

   --  values for Rst (remembering the possibility of 64-bit modular types) is

   --  from -2**63 to 2**64-1, and no run-time type has a big enough range.

   -----------------------

   -- Local Subprograms --

   -----------------------

   function Square_Mod_N (X, N : Int) return Int;

   pragma Inline (Square_Mod_N);

   --  Computes X**2 mod N avoiding intermediate overflow

   -----------

   -- Image --

   -----------

   function Image (Of_State : State) return String is

   begin

      return Int'Image (Of_State.X1) &

             ','                     &

             Int'Image (Of_State.X2) &

             ','                     &

             Int'Image (Of_State.Q);

   end Image;

   ------------

   -- Random --

   ------------

   function Random (Gen : Generator) return Rst is

      Genp : constant Pointer := Gen.Gen_State'Unrestricted_Access;

      Temp : Int;

      TF   : Flt;

   begin

      --  Check for flat range here, since we are typically run with checks

      --  off, note that in practice, this condition will usually be static

      --  so we will not actually generate any code for the normal case.

      if Rst'Last < Rst'First then

         raise Constraint_Error;

      end if;

      --  Continue with computation if non-flat range

      Genp.X1 := Square_Mod_N (Genp.X1, Genp.P);

      Genp.X2 := Square_Mod_N (Genp.X2, Genp.Q);

      Temp := Genp.X2 - Genp.X1;

      --  Following duplication is not an error, it is a loop unwinding!

      if Temp < 0 then

         Temp := Temp + Genp.Q;

      end if;

      if Temp < 0 then

         Temp := Temp + Genp.Q;

      end if;

      TF := Offs + (Flt (Temp) * Flt (Genp.P) + Flt (Genp.X1)) * Genp.Scl;

      --  Pathological, but there do exist cases where the rounding implicit

      --  in calculating the scale factor will cause rounding to 'Last + 1.

      --  In those cases, returning 'First results in the least bias.

      if TF >= Flt (Rst'Pos (Rst'Last)) + 0.5 then

         return Rst'First;

      elsif not Fits_In_32_Bits then

         return Rst'Val (Interfaces.Integer_64 (TF));

      else

         return Rst'Val (Int (TF));

      end if;

   end Random;

   -----------

   -- Reset --

   -----------

   procedure Reset (Gen : Generator; Initiator : Integer) is

      Genp   : constant Pointer := Gen.Gen_State'Unrestricted_Access;

      X1, X2 : Int;

   begin

      X1 := 2 + Int (Initiator) mod (K1 - 3);

      X2 := 2 + Int (Initiator) mod (K2 - 3);

      for J in 1 .. 5 loop

         X1 := Square_Mod_N (X1, K1);

         X2 := Square_Mod_N (X2, K2);

      end loop;

      --  Eliminate effects of small Initiators

      Genp.all :=

        (X1  => X1,

         X2  => X2,

         P   => K1,

         Q   => K2,

         FP  => K1F,

         Scl => Scal);

   end Reset;

   -----------

   -- Reset --

   -----------

   procedure Reset (Gen : Generator) is

      Genp : constant Pointer       := Gen.Gen_State'Unrestricted_Access;

      Now  : constant Calendar.Time := Calendar.Clock;

      X1   : Int;

      X2   : Int;

   begin

      X1 := Int (Calendar.Year    (Now)) * 12 * 31 +

            Int (Calendar.Month   (Now) * 31)     +

            Int (Calendar.Day     (Now));

      X2 := Int (Calendar.Seconds (Now) * Duration (1000.0));

      X1 := 2 + X1 mod (K1 - 3);

      X2 := 2 + X2 mod (K2 - 3);

      --  Eliminate visible effects of same day starts

      for J in 1 .. 5 loop

         X1 := Square_Mod_N (X1, K1);

         X2 := Square_Mod_N (X2, K2);

      end loop;

      Genp.all :=

        (X1  => X1,

         X2  => X2,

         P   => K1,

         Q   => K2,

         FP  => K1F,

         Scl => Scal);

   end Reset;

   -----------

   -- Reset --

   -----------

   procedure Reset (Gen : Generator; From_State : State) is

      Genp : constant Pointer := Gen.Gen_State'Unrestricted_Access;

   begin

      Genp.all := From_State;

   end Reset;

   ----------

   -- Save --

   ----------

   procedure Save (Gen : Generator; To_State : out State) is

   begin

      To_State := Gen.Gen_State;

   end Save;

   ------------------

   -- Square_Mod_N --

   ------------------

   function Square_Mod_N (X, N : Int) return Int is

   begin

      return Int ((Integer_64 (X) ** 2) mod (Integer_64 (N)));

   end Square_Mod_N;

   -----------

   -- Value --

   -----------

   function Value (Coded_State : String) return State is

      Last  : constant Natural := Coded_State'Last;

      Start : Positive := Coded_State'First;

      Stop  : Positive := Coded_State'First;

      Outs  : State;

   begin

      while Stop <= Last and then Coded_State (Stop) /= ',' loop

         Stop := Stop + 1;

      end loop;

      if Stop > Last then

         raise Constraint_Error;

      end if;

      Outs.X1 := Int'Value (Coded_State (Start .. Stop - 1));

      Start := Stop + 1;

      loop

         Stop := Stop + 1;

         exit when Stop > Last or else Coded_State (Stop) = ',';

      end loop;

      if Stop > Last then

         raise Constraint_Error;

      end if;

      Outs.X2  := Int'Value (Coded_State (Start .. Stop - 1));

      Outs.Q   := Int'Value (Coded_State (Stop + 1 .. Last));

      Outs.P   := Outs.Q * 2 + 1;

      Outs.FP  := Flt (Outs.P);

      Outs.Scl := (RstL - RstF + 1.0) / (Flt (Outs.P) * Flt (Outs.Q));

      --  Now do *some* sanity checks

      if Outs.Q < 31

        or else Outs.X1 not in 2 .. Outs.P - 1

        or else Outs.X2 not in 2 .. Outs.Q - 1

      then

         raise Constraint_Error;

      end if;

      return Outs;

   end Value;

end Ada.Numerics.Discrete_Random;