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-------------------------------------------------------------------------------
--- --
--- GNAT RUN-TIME COMPONENTS --
--- --
--- S Y S T E M . R A N D O M _ N U M B E R S --
--- --
--- B o d y --
--- --
--- Copyright (C) 2007,2009 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. --
--- --
-------------------------------------------------------------------------------
-
-------------------------------------------------------------------------------
--- --
--- The implementation here is derived from a C-program for MT19937, with --
--- initialization improved 2002/1/26. As required, the following notice is --
--- copied from the original program. --
--- --
--- Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura, --
--- All rights reserved. --
--- --
--- Redistribution and use in source and binary forms, with or without --
--- modification, are permitted provided that the following conditions --
--- are met: --
--- --
--- 1. Redistributions of source code must retain the above copyright --
--- notice, this list of conditions and the following disclaimer. --
--- --
--- 2. Redistributions in binary form must reproduce the above copyright --
--- notice, this list of conditions and the following disclaimer in the --
--- documentation and/or other materials provided with the distribution.--
--- --
--- 3. The names of its contributors may not be used to endorse or promote --
--- products derived from this software without specific prior written --
--- permission. --
--- --
--- THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS --
--- "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT --
--- LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR --
--- A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT --
--- OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, --
--- SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED --
--- TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR --
--- PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF --
--- LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING --
--- NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS --
--- SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. --
--- --
-------------------------------------------------------------------------------
-
-------------------------------------------------------------------------------
--- --
--- This is an implementation of the Mersenne Twister, twisted generalized --
--- feedback shift register of rational normal form, with state-bit --
--- reflection and tempering. This version generates 32-bit integers with a --
--- period of 2**19937 - 1 (a Mersenne prime, hence the name). For --
--- applications requiring more than 32 bits (up to 64), we concatenate two --
--- 32-bit numbers. --
--- --
--- See http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html for --
--- details. --
--- --
--- In contrast to the original code, we do not generate random numbers in --
--- batches of N. Measurement seems to show this has very little if any --
--- effect on performance, and it may be marginally better for real-time --
--- applications with hard deadlines. --
--- --
-------------------------------------------------------------------------------
-
-with Ada.Calendar; use Ada.Calendar;
-with Ada.Unchecked_Conversion;
-with Interfaces; use Interfaces;
-
-use Ada;
-
-package body System.Random_Numbers 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.
-
- Low31_Mask : constant := 2**31-1;
- Bit31_Mask : constant := 2**31;
-
- Matrix_A_X : constant array (State_Val range 0 .. 1) of State_Val :=
- (0, 16#9908b0df#);
-
- Y2K : constant Calendar.Time :=
- Calendar.Time_Of
- (Year => 2000, Month => 1, Day => 1, Seconds => 0.0);
- -- First Year 2000 day
-
- subtype Image_String is String (1 .. Max_Image_Width);
-
- -- Utility functions
-
- procedure Init (Gen : out Generator; Initiator : Unsigned_32);
- -- Perform a default initialization of the state of Gen. The resulting
- -- state is identical for identical values of Initiator.
-
- procedure Insert_Image
- (S : in out Image_String;
- Index : Integer;
- V : State_Val);
- -- Insert image of V into S, in the Index'th 11-character substring
-
- function Extract_Value (S : String; Index : Integer) return State_Val;
- -- Treat S as a sequence of 11-character decimal numerals and return
- -- the result of converting numeral #Index (numbering from 0)
-
- function To_Unsigned is
- new Unchecked_Conversion (Integer_32, Unsigned_32);
- function To_Unsigned is
- new Unchecked_Conversion (Integer_64, Unsigned_64);
-
- ------------
- -- Random --
- ------------
-
- function Random (Gen : Generator) return Unsigned_32 is
- G : Generator renames Gen'Unrestricted_Access.all;
- Y : State_Val;
- I : Integer;
-
- begin
- I := G.I;
-
- if I < N - M then
- Y := (G.S (I) and Bit31_Mask) or (G.S (I + 1) and Low31_Mask);
- Y := G.S (I + M) xor Shift_Right (Y, 1) xor Matrix_A_X (Y and 1);
- I := I + 1;
-
- elsif I < N - 1 then
- Y := (G.S (I) and Bit31_Mask) or (G.S (I + 1) and Low31_Mask);
- Y := G.S (I + (M - N))
- xor Shift_Right (Y, 1)
- xor Matrix_A_X (Y and 1);
- I := I + 1;
-
- elsif I = N - 1 then
- Y := (G.S (I) and Bit31_Mask) or (G.S (0) and Low31_Mask);
- Y := G.S (M - 1) xor Shift_Right (Y, 1) xor Matrix_A_X (Y and 1);
- I := 0;
-
- else
- Init (G, 5489);
- return Random (Gen);
- end if;
-
- G.S (G.I) := Y;
- G.I := I;
-
- Y := Y xor Shift_Right (Y, 11);
- Y := Y xor (Shift_Left (Y, 7) and 16#9d2c5680#);
- Y := Y xor (Shift_Left (Y, 15) and 16#efc60000#);
- Y := Y xor Shift_Right (Y, 18);
-
- return Y;
- end Random;
-
- function Random (Gen : Generator) return Float is
-
- -- Note: The application of Float'Machine (...) is necessary to avoid
- -- returning extra significand bits. Without it, the function's value
- -- will change if it is spilled, for example, causing
- -- gratuitous nondeterminism.
-
- Result : constant Float :=
- Float'Machine
- (Float (Unsigned_32'(Random (Gen))) * 2.0 ** (-32));
- begin
- if Result < 1.0 then
- return Result;
- else
- return Float'Adjacent (1.0, 0.0);
- end if;
- end Random;
-
- function Random (Gen : Generator) return Long_Float is
- Result : constant Long_Float :=
- Long_Float'Machine ((Long_Float (Unsigned_32'(Random (Gen)))
- * 2.0 ** (-32))
- + (Long_Float (Unsigned_32'(Random (Gen))) * 2.0 ** (-64)));
- begin
- if Result < 1.0 then
- return Result;
- else
- return Long_Float'Adjacent (1.0, 0.0);
- end if;
- end Random;
-
- function Random (Gen : Generator) return Unsigned_64 is
- begin
- return Shift_Left (Unsigned_64 (Unsigned_32'(Random (Gen))), 32)
- or Unsigned_64 (Unsigned_32'(Random (Gen)));
- end Random;
-
- ---------------------
- -- Random_Discrete --
- ---------------------
-
- function Random_Discrete
- (Gen : Generator;
- Min : Result_Subtype := Default_Min;
- Max : Result_Subtype := Result_Subtype'Last) return Result_Subtype
- is
- begin
- if Max = Min then
- return Max;
-
- elsif Max < Min then
- raise Constraint_Error;
-
- elsif Result_Subtype'Base'Size > 32 then
- declare
- -- In the 64-bit case, we have to be careful, since not all 64-bit
- -- unsigned values are representable in GNAT's root_integer type.
- -- Ignore different-size warnings here; since GNAT's handling
- -- is correct.
-
- pragma Warnings ("Z");
- function Conv_To_Unsigned is
- new Unchecked_Conversion (Result_Subtype'Base, Unsigned_64);
- function Conv_To_Result is
- new Unchecked_Conversion (Unsigned_64, Result_Subtype'Base);
- pragma Warnings ("z");
-
- N : constant Unsigned_64 :=
- Conv_To_Unsigned (Max) - Conv_To_Unsigned (Min) + 1;
-
- X, Slop : Unsigned_64;
-
- begin
- if N = 0 then
- return Conv_To_Result (Conv_To_Unsigned (Min) + Random (Gen));
-
- else
- Slop := Unsigned_64'Last rem N + 1;
-
- loop
- X := Random (Gen);
- exit when Slop = N or else X <= Unsigned_64'Last - Slop;
- end loop;
-
- return Conv_To_Result (Conv_To_Unsigned (Min) + X rem N);
- end if;
- end;
-
- elsif Result_Subtype'Pos (Max) - Result_Subtype'Pos (Min) =
- 2 ** 32 - 1
- then
- return Result_Subtype'Val
- (Result_Subtype'Pos (Min) + Unsigned_32'Pos (Random (Gen)));
- else
- declare
- N : constant Unsigned_32 :=
- Unsigned_32 (Result_Subtype'Pos (Max) -
- Result_Subtype'Pos (Min) + 1);
- Slop : constant Unsigned_32 := Unsigned_32'Last rem N + 1;
- X : Unsigned_32;
-
- begin
- loop
- X := Random (Gen);
- exit when Slop = N or else X <= Unsigned_32'Last - Slop;
- end loop;
-
- return
- Result_Subtype'Val
- (Result_Subtype'Pos (Min) + Unsigned_32'Pos (X rem N));
- end;
- end if;
- end Random_Discrete;
-
- ------------------
- -- Random_Float --
- ------------------
-
- function Random_Float (Gen : Generator) return Result_Subtype is
- begin
- if Result_Subtype'Base'Digits > Float'Digits then
- return Result_Subtype'Machine (Result_Subtype
- (Long_Float'(Random (Gen))));
- else
- return Result_Subtype'Machine (Result_Subtype
- (Float'(Random (Gen))));
- end if;
- end Random_Float;
-
- -----------
- -- Reset --
- -----------
-
- procedure Reset (Gen : out Generator) is
- X : constant Unsigned_32 := Unsigned_32 ((Calendar.Clock - Y2K) * 64.0);
- begin
- Init (Gen, X);
- end Reset;
-
- procedure Reset (Gen : out Generator; Initiator : Integer_32) is
- begin
- Init (Gen, To_Unsigned (Initiator));
- end Reset;
-
- procedure Reset (Gen : out Generator; Initiator : Unsigned_32) is
- begin
- Init (Gen, Initiator);
- end Reset;
-
- procedure Reset (Gen : out Generator; Initiator : Integer) is
- begin
- pragma Warnings ("C");
- -- This is probably an unnecessary precaution against future change, but
- -- since the test is a static expression, no extra code is involved.
-
- if Integer'Size <= 32 then
- Init (Gen, To_Unsigned (Integer_32 (Initiator)));
-
- else
- declare
- Initiator1 : constant Unsigned_64 :=
- To_Unsigned (Integer_64 (Initiator));
- Init0 : constant Unsigned_32 :=
- Unsigned_32 (Initiator1 mod 2 ** 32);
- Init1 : constant Unsigned_32 :=
- Unsigned_32 (Shift_Right (Initiator1, 32));
- begin
- Reset (Gen, Initialization_Vector'(Init0, Init1));
- end;
- end if;
-
- pragma Warnings ("c");
- end Reset;
-
- procedure Reset (Gen : out Generator; Initiator : Initialization_Vector) is
- I, J : Integer;
-
- begin
- Init (Gen, 19650218);
- I := 1;
- J := 0;
-
- if Initiator'Length > 0 then
- for K in reverse 1 .. Integer'Max (N, Initiator'Length) loop
- Gen.S (I) :=
- (Gen.S (I)
- xor ((Gen.S (I - 1) xor Shift_Right (Gen.S (I - 1), 30))
- * 1664525))
- + Initiator (J + Initiator'First) + Unsigned_32 (J);
-
- I := I + 1;
- J := J + 1;
-
- if I >= N then
- Gen.S (0) := Gen.S (N - 1);
- I := 1;
- end if;
-
- if J >= Initiator'Length then
- J := 0;
- end if;
- end loop;
- end if;
-
- for K in reverse 1 .. N - 1 loop
- Gen.S (I) :=
- (Gen.S (I) xor ((Gen.S (I - 1)
- xor Shift_Right (Gen.S (I - 1), 30)) * 1566083941))
- - Unsigned_32 (I);
- I := I + 1;
-
- if I >= N then
- Gen.S (0) := Gen.S (N - 1);
- I := 1;
- end if;
- end loop;
-
- Gen.S (0) := Bit31_Mask;
- end Reset;
-
- procedure Reset (Gen : out Generator; From_State : Generator) is
- begin
- Gen.S := From_State.S;
- Gen.I := From_State.I;
- end Reset;
-
- procedure Reset (Gen : out Generator; From_State : State) is
- begin
- Gen.I := 0;
- Gen.S := From_State;
- end Reset;
-
- procedure Reset (Gen : out Generator; From_Image : String) is
- begin
- Gen.I := 0;
-
- for J in 0 .. N - 1 loop
- Gen.S (J) := Extract_Value (From_Image, J);
- end loop;
- end Reset;
-
- ----------
- -- Save --
- ----------
-
- procedure Save (Gen : Generator; To_State : out State) is
- Gen2 : Generator;
-
- begin
- if Gen.I = N then
- Init (Gen2, 5489);
- To_State := Gen2.S;
-
- else
- To_State (0 .. N - 1 - Gen.I) := Gen.S (Gen.I .. N - 1);
- To_State (N - Gen.I .. N - 1) := Gen.S (0 .. Gen.I - 1);
- end if;
- end Save;
-
- -----------
- -- Image --
- -----------
-
- function Image (Of_State : State) return String is
- Result : Image_String;
-
- begin
- Result := (others => ' ');
-
- for J in Of_State'Range loop
- Insert_Image (Result, J, Of_State (J));
- end loop;
-
- return Result;
- end Image;
-
- function Image (Gen : Generator) return String is
- Result : Image_String;
-
- begin
- Result := (others => ' ');
-
- for J in 0 .. N - 1 loop
- Insert_Image (Result, J, Gen.S ((J + Gen.I) mod N));
- end loop;
-
- return Result;
- end Image;
-
- -----------
- -- Value --
- -----------
-
- function Value (Coded_State : String) return State is
- Gen : Generator;
- S : State;
- begin
- Reset (Gen, Coded_State);
- Save (Gen, S);
- return S;
- end Value;
-
- ----------
- -- Init --
- ----------
-
- procedure Init (Gen : out Generator; Initiator : Unsigned_32) is
- begin
- Gen.S (0) := Initiator;
-
- for I in 1 .. N - 1 loop
- Gen.S (I) :=
- 1812433253
- * (Gen.S (I - 1) xor Shift_Right (Gen.S (I - 1), 30))
- + Unsigned_32 (I);
- end loop;
-
- Gen.I := 0;
- end Init;
-
- ------------------
- -- Insert_Image --
- ------------------
-
- procedure Insert_Image
- (S : in out Image_String;
- Index : Integer;
- V : State_Val)
- is
- Value : constant String := State_Val'Image (V);
- begin
- S (Index * 11 + 1 .. Index * 11 + Value'Length) := Value;
- end Insert_Image;
-
- -------------------
- -- Extract_Value --
- -------------------
-
- function Extract_Value (S : String; Index : Integer) return State_Val is
- begin
- return State_Val'Value (S (S'First + Index * 11 ..
- S'First + Index * 11 + 11));
- end Extract_Value;
-
-end System.Random_Numbers;