1 ------------------------------------------------------------------------------
3 -- GNAT RUN-TIME COMPONENTS --
5 -- S Y S T E M . R A N D O M _ N U M B E R S --
9 -- Copyright (C) 2007-2019, Free Software Foundation, Inc. --
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. --
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. --
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/>. --
27 -- GNAT was originally developed by the GNAT team at New York University. --
28 -- Extensive contributions were provided by Ada Core Technologies Inc. --
30 ------------------------------------------------------------------------------
32 ------------------------------------------------------------------------------
34 -- The implementation here is derived from a C-program for MT19937, with --
35 -- initialization improved 2002/1/26. As required, the following notice is --
36 -- copied from the original program. --
38 -- Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura, --
39 -- All rights reserved. --
41 -- Redistribution and use in source and binary forms, with or without --
42 -- modification, are permitted provided that the following conditions --
45 -- 1. Redistributions of source code must retain the above copyright --
46 -- notice, this list of conditions and the following disclaimer. --
48 -- 2. Redistributions in binary form must reproduce the above copyright --
49 -- notice, this list of conditions and the following disclaimer in the --
50 -- documentation and/or other materials provided with the distribution.--
52 -- 3. The names of its contributors may not be used to endorse or promote --
53 -- products derived from this software without specific prior written --
56 -- THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS --
57 -- "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT --
58 -- LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR --
59 -- A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT --
60 -- OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, --
61 -- SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED --
62 -- TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR --
63 -- PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF --
64 -- LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING --
65 -- NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS --
66 -- SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. --
68 ------------------------------------------------------------------------------
70 ------------------------------------------------------------------------------
72 -- This is an implementation of the Mersenne Twister, twisted generalized --
73 -- feedback shift register of rational normal form, with state-bit --
74 -- reflection and tempering. This version generates 32-bit integers with a --
75 -- period of 2**19937 - 1 (a Mersenne prime, hence the name). For --
76 -- applications requiring more than 32 bits (up to 64), we concatenate two --
79 -- See http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html for --
82 -- In contrast to the original code, we do not generate random numbers in --
83 -- batches of N. Measurement seems to show this has very little if any --
84 -- effect on performance, and it may be marginally better for real-time --
85 -- applications with hard deadlines. --
87 ------------------------------------------------------------------------------
89 with Ada.Unchecked_Conversion;
91 with System.Random_Seed;
93 with Interfaces; use Interfaces;
97 package body System.Random_Numbers with
100 Image_Numeral_Length : constant := Max_Image_Width / N;
102 subtype Image_String is String (1 .. Max_Image_Width);
104 ----------------------------
105 -- Algorithmic Parameters --
106 ----------------------------
108 Lower_Mask : constant := 2**31 - 1;
109 Upper_Mask : constant := 2**31;
111 Matrix_A : constant array (State_Val range 0 .. 1) of State_Val
112 := (0, 16#9908b0df#);
113 -- The twist transformation is represented by a matrix of the form
118 -- where 0 is a 31x31 block of 0s, I(31) is the 31x31 identity matrix and
119 -- _a is a particular bit row-vector, represented here by a 32-bit integer.
120 -- If integer x represents a row vector of bits (with x(0), the units bit,
122 -- x * A = [0 x(31..1)] xor Matrix_A(x(0)).
126 B_Mask : constant := 16#9d2c5680#;
128 C_Mask : constant := 16#efc60000#;
130 -- The tempering shifts and bit masks, in the order applied
132 Seed0 : constant := 5489;
133 -- Default seed, used to initialize the state vector when Reset not called
135 Seed1 : constant := 19650218;
136 -- Seed used to initialize the state vector when calling Reset with an
137 -- initialization vector.
139 Mult0 : constant := 1812433253;
140 -- Multiplier for a modified linear congruential generator used to
141 -- initialize the state vector when calling Reset with a single integer
144 Mult1 : constant := 1664525;
145 Mult2 : constant := 1566083941;
146 -- Multipliers for two modified linear congruential generators used to
147 -- initialize the state vector when calling Reset with an initialization
150 -----------------------
151 -- Local Subprograms --
152 -----------------------
154 procedure Init (Gen : Generator; Initiator : Unsigned_32);
155 -- Perform a default initialization of the state of Gen. The resulting
156 -- state is identical for identical values of Initiator.
158 procedure Insert_Image
159 (S : in out Image_String;
162 -- Insert image of V into S, in the Index'th 11-character substring
164 function Extract_Value (S : String; Index : Integer) return State_Val;
165 -- Treat S as a sequence of 11-character decimal numerals and return
166 -- the result of converting numeral #Index (numbering from 0)
168 function To_Unsigned is
169 new Unchecked_Conversion (Integer_32, Unsigned_32);
170 function To_Unsigned is
171 new Unchecked_Conversion (Integer_64, Unsigned_64);
177 function Random (Gen : Generator) return Unsigned_32 is
178 G : Generator renames Gen.Writable.Self.all;
180 I : Integer; -- should avoid use of identifier I ???
186 Y := (G.S (I) and Upper_Mask) or (G.S (I + 1) and Lower_Mask);
187 Y := G.S (I + M) xor Shift_Right (Y, 1) xor Matrix_A (Y and 1);
191 Y := (G.S (I) and Upper_Mask) or (G.S (I + 1) and Lower_Mask);
192 Y := G.S (I + (M - N))
193 xor Shift_Right (Y, 1)
194 xor Matrix_A (Y and 1);
198 Y := (G.S (I) and Upper_Mask) or (G.S (0) and Lower_Mask);
199 Y := G.S (M - 1) xor Shift_Right (Y, 1) xor Matrix_A (Y and 1);
210 Y := Y xor Shift_Right (Y, U);
211 Y := Y xor (Shift_Left (Y, S) and B_Mask);
212 Y := Y xor (Shift_Left (Y, T) and C_Mask);
213 Y := Y xor Shift_Right (Y, L);
219 type Unsigned is mod <>;
220 type Real is digits <>;
221 with function Random (G : Generator) return Unsigned is <>;
222 function Random_Float_Template (Gen : Generator) return Real;
223 pragma Inline (Random_Float_Template);
224 -- Template for a random-number generator implementation that delivers
225 -- values of type Real in the range [0 .. 1], using values from Gen,
226 -- assuming that Unsigned is large enough to hold the bits of a mantissa
229 ---------------------------
230 -- Random_Float_Template --
231 ---------------------------
233 function Random_Float_Template (Gen : Generator) return Real is
235 pragma Compile_Time_Error
236 (Unsigned'Last <= 2**(Real'Machine_Mantissa - 1),
237 "insufficiently large modular type used to hold mantissa");
240 -- This code generates random floating-point numbers from unsigned
241 -- integers. Assuming that Real'Machine_Radix = 2, it can deliver all
242 -- machine values of type Real (as implied by Real'Machine_Mantissa and
243 -- Real'Machine_Emin), which is not true of the standard method (to
244 -- which we fall back for nonbinary radix): computing Real(<random
245 -- integer>) / (<max random integer>+1). To do so, we first extract an
246 -- (M-1)-bit significand (where M is Real'Machine_Mantissa), and then
247 -- decide on a normalized exponent by repeated coin flips, decrementing
248 -- from 0 as long as we flip heads (1 bits). This process yields the
249 -- proper geometric distribution for the exponent: in a uniformly
250 -- distributed set of floating-point numbers, 1/2 of them will be in
251 -- (0.5, 1], 1/4 will be in (0.25, 0.5], and so forth. It makes a
252 -- further adjustment at binade boundaries (see comments below) to give
253 -- the effect of selecting a uniformly distributed real deviate in
254 -- [0..1] and then rounding to the nearest representable floating-point
255 -- number. The algorithm attempts to be stingy with random integers. In
256 -- the worst case, it can consume roughly -Real'Machine_Emin/32 32-bit
257 -- integers, but this case occurs with probability around
258 -- 2**Machine_Emin, and the expected number of calls to integer-valued
259 -- Random is 1. For another discussion of the issues addressed by this
260 -- process, see Allen Downey's unpublished paper at
261 -- http://allendowney.com/research/rand/downey07randfloat.pdf.
263 if Real'Machine_Radix /= 2 then
265 (Real (Unsigned'(Random (Gen))) * 2.0**(-Unsigned'Size));
269 type Bit_Count is range 0 .. 4;
271 subtype T is Real'Base;
273 Trailing_Ones : constant array (Unsigned_32 range 0 .. 15)
275 (2#00000# => 0, 2#00001# => 1, 2#00010# => 0, 2#00011# => 2,
276 2#00100# => 0, 2#00101# => 1, 2#00110# => 0, 2#00111# => 3,
277 2#01000# => 0, 2#01001# => 1, 2#01010# => 0, 2#01011# => 2,
278 2#01100# => 0, 2#01101# => 1, 2#01110# => 0, 2#01111# => 4);
280 Pow_Tab : constant array (Bit_Count range 0 .. 3) of Real
281 := (0 => 2.0**(0 - T'Machine_Mantissa),
282 1 => 2.0**(-1 - T'Machine_Mantissa),
283 2 => 2.0**(-2 - T'Machine_Mantissa),
284 3 => 2.0**(-3 - T'Machine_Mantissa));
286 Extra_Bits : constant Natural :=
287 (Unsigned'Size - T'Machine_Mantissa + 1);
288 -- Random bits left over after selecting mantissa
292 X : Real; -- Scaled mantissa
293 R : Unsigned_32; -- Supply of random bits
294 R_Bits : Natural; -- Number of bits left in R
295 K : Bit_Count; -- Next decrement to exponent
299 Mantissa := Random (Gen) / 2**Extra_Bits;
300 R := Unsigned_32 (Mantissa mod 2**Extra_Bits);
301 R_Bits := Extra_Bits;
302 X := Real (2**(T'Machine_Mantissa - 1) + Mantissa); -- Exact
304 if Extra_Bits < 4 and then R < 2 ** Extra_Bits - 1 then
306 -- We got lucky and got a zero in our few extra bits
308 K := Trailing_Ones (R);
313 -- R has R_Bits unprocessed random bits, a multiple of 4.
314 -- X needs to be halved for each trailing one bit. The
315 -- process stops as soon as a 0 bit is found. If R_Bits
316 -- becomes zero, reload R.
318 -- Process 4 bits at a time for speed: the two iterations
319 -- on average with three tests each was still too slow,
320 -- probably because the branches are not predictable.
321 -- This loop now will only execute once 94% of the cases,
322 -- doing more bits at a time will not help.
324 while R_Bits >= 4 loop
325 K := Trailing_Ones (R mod 16);
327 exit Find_Zero when K < 4; -- Exits 94% of the time
329 R_Bits := R_Bits - 4;
334 -- Do not allow us to loop endlessly even in the (very
335 -- unlikely) case that Random (Gen) keeps yielding all ones.
337 exit Find_Zero when X = 0.0;
343 -- K has the count of trailing ones not reflected yet in X. The
344 -- following multiplication takes care of that, as well as the
345 -- correction to move the radix point to the left of the mantissa.
346 -- Doing it at the end avoids repeated rounding errors in the
347 -- exceedingly unlikely case of ever having a subnormal result.
349 X := X * Pow_Tab (K);
351 -- The smallest value in each binade is rounded to by 0.75 of
352 -- the span of real numbers as its next larger neighbor, and
353 -- 1.0 is rounded to by half of the span of real numbers as its
354 -- next smaller neighbor. To account for this, when we encounter
355 -- the smallest number in a binade, we substitute the smallest
356 -- value in the next larger binade with probability 1/2.
358 if Mantissa = 0 and then Unsigned_32'(Random (Gen)) mod 2 = 0 then
365 end Random_Float_Template;
371 function Random (Gen : Generator) return Float is
372 function F is new Random_Float_Template (Unsigned_32, Float);
377 function Random (Gen : Generator) return Long_Float is
378 function F is new Random_Float_Template (Unsigned_64, Long_Float);
383 function Random (Gen : Generator) return Unsigned_64 is
385 return Shift_Left (Unsigned_64 (Unsigned_32'(Random (Gen))), 32)
386 or Unsigned_64 (Unsigned_32'(Random (Gen)));
389 ---------------------
390 -- Random_Discrete --
391 ---------------------
393 function Random_Discrete
395 Min : Result_Subtype := Default_Min;
396 Max : Result_Subtype := Result_Subtype'Last) return Result_Subtype
403 raise Constraint_Error;
405 elsif Result_Subtype'Base'Size > 32 then
407 -- In the 64-bit case, we have to be careful, since not all 64-bit
408 -- unsigned values are representable in GNAT's root_integer type.
409 -- Ignore different-size warnings here since GNAT's handling
412 pragma Warnings ("Z");
413 function Conv_To_Unsigned is
414 new Unchecked_Conversion (Result_Subtype'Base, Unsigned_64);
415 function Conv_To_Result is
416 new Unchecked_Conversion (Unsigned_64, Result_Subtype'Base);
417 pragma Warnings ("z");
419 N : constant Unsigned_64 :=
420 Conv_To_Unsigned (Max) - Conv_To_Unsigned (Min) + 1;
422 X, Slop : Unsigned_64;
426 return Conv_To_Result (Conv_To_Unsigned (Min) + Random (Gen));
429 Slop := Unsigned_64'Last rem N + 1;
433 exit when Slop = N or else X <= Unsigned_64'Last - Slop;
436 return Conv_To_Result (Conv_To_Unsigned (Min) + X rem N);
440 elsif Result_Subtype'Pos (Max) - Result_Subtype'Pos (Min) =
443 return Result_Subtype'Val
444 (Result_Subtype'Pos (Min) + Unsigned_32'Pos (Random (Gen)));
447 N : constant Unsigned_32 :=
448 Unsigned_32 (Result_Subtype'Pos (Max) -
449 Result_Subtype'Pos (Min) + 1);
450 Slop : constant Unsigned_32 := Unsigned_32'Last rem N + 1;
456 exit when Slop = N or else X <= Unsigned_32'Last - Slop;
461 (Result_Subtype'Pos (Min) + Unsigned_32'Pos (X rem N));
470 function Random_Float (Gen : Generator) return Result_Subtype is
472 if Result_Subtype'Base'Digits > Float'Digits then
473 return Result_Subtype'Machine (Result_Subtype
474 (Long_Float'(Random (Gen))));
476 return Result_Subtype'Machine (Result_Subtype
477 (Float'(Random (Gen))));
485 procedure Reset (Gen : Generator) is
487 Init (Gen, Unsigned_32'Mod (Random_Seed.Get_Seed));
490 procedure Reset (Gen : Generator; Initiator : Integer_32) is
492 Init (Gen, To_Unsigned (Initiator));
495 procedure Reset (Gen : Generator; Initiator : Unsigned_32) is
497 Init (Gen, Initiator);
500 procedure Reset (Gen : Generator; Initiator : Integer) is
502 -- This is probably an unnecessary precaution against future change, but
503 -- since the test is a static expression, no extra code is involved.
505 if Integer'Size <= 32 then
506 Init (Gen, To_Unsigned (Integer_32 (Initiator)));
510 Initiator1 : constant Unsigned_64 :=
511 To_Unsigned (Integer_64 (Initiator));
512 Init0 : constant Unsigned_32 :=
513 Unsigned_32 (Initiator1 mod 2 ** 32);
514 Init1 : constant Unsigned_32 :=
515 Unsigned_32 (Shift_Right (Initiator1, 32));
517 Reset (Gen, Initialization_Vector'(Init0, Init1));
522 procedure Reset (Gen : Generator; Initiator : Initialization_Vector) is
523 G : Generator renames Gen.Writable.Self.all;
531 if Initiator'Length > 0 then
532 for K in reverse 1 .. Integer'Max (N, Initiator'Length) loop
534 (G.S (I) xor ((G.S (I - 1)
535 xor Shift_Right (G.S (I - 1), 30)) * Mult1))
536 + Initiator (J + Initiator'First) + Unsigned_32 (J);
542 G.S (0) := G.S (N - 1);
546 if J >= Initiator'Length then
552 for K in reverse 1 .. N - 1 loop
554 (G.S (I) xor ((G.S (I - 1)
555 xor Shift_Right (G.S (I - 1), 30)) * Mult2))
560 G.S (0) := G.S (N - 1);
565 G.S (0) := Upper_Mask;
568 procedure Reset (Gen : Generator; From_State : Generator) is
569 G : Generator renames Gen.Writable.Self.all;
575 procedure Reset (Gen : Generator; From_State : State) is
576 G : Generator renames Gen.Writable.Self.all;
582 procedure Reset (Gen : Generator; From_Image : String) is
583 G : Generator renames Gen.Writable.Self.all;
587 for J in 0 .. N - 1 loop
588 G.S (J) := Extract_Value (From_Image, J);
596 procedure Save (Gen : Generator; To_State : out State) is
605 To_State (0 .. N - 1 - Gen.I) := Gen.S (Gen.I .. N - 1);
606 To_State (N - Gen.I .. N - 1) := Gen.S (0 .. Gen.I - 1);
614 function Image (Of_State : State) return String is
615 Result : Image_String;
618 Result := (others => ' ');
620 for J in Of_State'Range loop
621 Insert_Image (Result, J, Of_State (J));
627 function Image (Gen : Generator) return String is
628 Result : Image_String;
631 Result := (others => ' ');
632 for J in 0 .. N - 1 loop
633 Insert_Image (Result, J, Gen.S ((J + Gen.I) mod N));
643 function Value (Coded_State : String) return State is
647 Reset (Gen, Coded_State);
656 procedure Init (Gen : Generator; Initiator : Unsigned_32) is
657 G : Generator renames Gen.Writable.Self.all;
659 G.S (0) := Initiator;
661 for I in 1 .. N - 1 loop
663 (G.S (I - 1) xor Shift_Right (G.S (I - 1), 30)) * Mult0
674 procedure Insert_Image
675 (S : in out Image_String;
679 Value : constant String := State_Val'Image (V);
681 S (Index * 11 + 1 .. Index * 11 + Value'Length) := Value;
688 function Extract_Value (S : String; Index : Integer) return State_Val is
689 Start : constant Integer := S'First + Index * Image_Numeral_Length;
691 return State_Val'Value (S (Start .. Start + Image_Numeral_Length - 1));
694 end System.Random_Numbers;