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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;
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