1------------------------------------------------------------------------------ 2-- -- 3-- GNAT RUN-TIME COMPONENTS -- 4-- -- 5-- S Y S T E M . R A N D O M _ N U M B E R S -- 6-- -- 7-- B o d y -- 8-- -- 9-- Copyright (C) 2007-2012, 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------------------------------------------------------------------------------ 33-- -- 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. -- 37-- -- 38-- Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura, -- 39-- All rights reserved. -- 40-- -- 41-- Redistribution and use in source and binary forms, with or without -- 42-- modification, are permitted provided that the following conditions -- 43-- are met: -- 44-- -- 45-- 1. Redistributions of source code must retain the above copyright -- 46-- notice, this list of conditions and the following disclaimer. -- 47-- -- 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.-- 51-- -- 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 -- 54-- permission. -- 55-- -- 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. -- 67-- -- 68------------------------------------------------------------------------------ 69 70------------------------------------------------------------------------------ 71-- -- 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 -- 77-- 32-bit numbers. -- 78-- -- 79-- See http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html for -- 80-- details. -- 81-- -- 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. -- 86-- -- 87------------------------------------------------------------------------------ 88 89with Ada.Unchecked_Conversion; 90 91with System.Random_Seed; 92 93with Interfaces; use Interfaces; 94 95use Ada; 96 97package body System.Random_Numbers is 98 99 Image_Numeral_Length : constant := Max_Image_Width / N; 100 subtype Image_String is String (1 .. Max_Image_Width); 101 102 ---------------------------- 103 -- Algorithmic Parameters -- 104 ---------------------------- 105 106 Lower_Mask : constant := 2**31-1; 107 Upper_Mask : constant := 2**31; 108 109 Matrix_A : constant array (State_Val range 0 .. 1) of State_Val 110 := (0, 16#9908b0df#); 111 -- The twist transformation is represented by a matrix of the form 112 -- 113 -- [ 0 I(31) ] 114 -- [ _a ] 115 -- 116 -- where 0 is a 31x31 block of 0s, I(31) is the 31x31 identity matrix and 117 -- _a is a particular bit row-vector, represented here by a 32-bit integer. 118 -- If integer x represents a row vector of bits (with x(0), the units bit, 119 -- last), then 120 -- x * A = [0 x(31..1)] xor Matrix_A(x(0)). 121 122 U : constant := 11; 123 S : constant := 7; 124 B_Mask : constant := 16#9d2c5680#; 125 T : constant := 15; 126 C_Mask : constant := 16#efc60000#; 127 L : constant := 18; 128 -- The tempering shifts and bit masks, in the order applied 129 130 Seed0 : constant := 5489; 131 -- Default seed, used to initialize the state vector when Reset not called 132 133 Seed1 : constant := 19650218; 134 -- Seed used to initialize the state vector when calling Reset with an 135 -- initialization vector. 136 137 Mult0 : constant := 1812433253; 138 -- Multiplier for a modified linear congruential generator used to 139 -- initialize the state vector when calling Reset with a single integer 140 -- seed. 141 142 Mult1 : constant := 1664525; 143 Mult2 : constant := 1566083941; 144 -- Multipliers for two modified linear congruential generators used to 145 -- initialize the state vector when calling Reset with an initialization 146 -- vector. 147 148 ----------------------- 149 -- Local Subprograms -- 150 ----------------------- 151 152 procedure Init (Gen : Generator; Initiator : Unsigned_32); 153 -- Perform a default initialization of the state of Gen. The resulting 154 -- state is identical for identical values of Initiator. 155 156 procedure Insert_Image 157 (S : in out Image_String; 158 Index : Integer; 159 V : State_Val); 160 -- Insert image of V into S, in the Index'th 11-character substring 161 162 function Extract_Value (S : String; Index : Integer) return State_Val; 163 -- Treat S as a sequence of 11-character decimal numerals and return 164 -- the result of converting numeral #Index (numbering from 0) 165 166 function To_Unsigned is 167 new Unchecked_Conversion (Integer_32, Unsigned_32); 168 function To_Unsigned is 169 new Unchecked_Conversion (Integer_64, Unsigned_64); 170 171 ------------ 172 -- Random -- 173 ------------ 174 175 function Random (Gen : Generator) return Unsigned_32 is 176 G : Generator renames Gen.Writable.Self.all; 177 Y : State_Val; 178 I : Integer; -- should avoid use of identifier I ??? 179 180 begin 181 I := G.I; 182 183 if I < N - M then 184 Y := (G.S (I) and Upper_Mask) or (G.S (I + 1) and Lower_Mask); 185 Y := G.S (I + M) xor Shift_Right (Y, 1) xor Matrix_A (Y and 1); 186 I := I + 1; 187 188 elsif I < N - 1 then 189 Y := (G.S (I) and Upper_Mask) or (G.S (I + 1) and Lower_Mask); 190 Y := G.S (I + (M - N)) 191 xor Shift_Right (Y, 1) 192 xor Matrix_A (Y and 1); 193 I := I + 1; 194 195 elsif I = N - 1 then 196 Y := (G.S (I) and Upper_Mask) or (G.S (0) and Lower_Mask); 197 Y := G.S (M - 1) xor Shift_Right (Y, 1) xor Matrix_A (Y and 1); 198 I := 0; 199 200 else 201 Init (G, Seed0); 202 return Random (Gen); 203 end if; 204 205 G.S (G.I) := Y; 206 G.I := I; 207 208 Y := Y xor Shift_Right (Y, U); 209 Y := Y xor (Shift_Left (Y, S) and B_Mask); 210 Y := Y xor (Shift_Left (Y, T) and C_Mask); 211 Y := Y xor Shift_Right (Y, L); 212 213 return Y; 214 end Random; 215 216 generic 217 type Unsigned is mod <>; 218 type Real is digits <>; 219 with function Random (G : Generator) return Unsigned is <>; 220 function Random_Float_Template (Gen : Generator) return Real; 221 pragma Inline (Random_Float_Template); 222 -- Template for a random-number generator implementation that delivers 223 -- values of type Real in the range [0 .. 1], using values from Gen, 224 -- assuming that Unsigned is large enough to hold the bits of a mantissa 225 -- for type Real. 226 227 --------------------------- 228 -- Random_Float_Template -- 229 --------------------------- 230 231 function Random_Float_Template (Gen : Generator) return Real is 232 233 pragma Compile_Time_Error 234 (Unsigned'Last <= 2**(Real'Machine_Mantissa - 1), 235 "insufficiently large modular type used to hold mantissa"); 236 237 begin 238 -- This code generates random floating-point numbers from unsigned 239 -- integers. Assuming that Real'Machine_Radix = 2, it can deliver all 240 -- machine values of type Real (as implied by Real'Machine_Mantissa and 241 -- Real'Machine_Emin), which is not true of the standard method (to 242 -- which we fall back for non-binary radix): computing Real(<random 243 -- integer>) / (<max random integer>+1). To do so, we first extract an 244 -- (M-1)-bit significand (where M is Real'Machine_Mantissa), and then 245 -- decide on a normalized exponent by repeated coin flips, decrementing 246 -- from 0 as long as we flip heads (1 bits). This process yields the 247 -- proper geometric distribution for the exponent: in a uniformly 248 -- distributed set of floating-point numbers, 1/2 of them will be in 249 -- (0.5, 1], 1/4 will be in (0.25, 0.5], and so forth. It makes a 250 -- further adjustment at binade boundaries (see comments below) to give 251 -- the effect of selecting a uniformly distributed real deviate in 252 -- [0..1] and then rounding to the nearest representable floating-point 253 -- number. The algorithm attempts to be stingy with random integers. In 254 -- the worst case, it can consume roughly -Real'Machine_Emin/32 32-bit 255 -- integers, but this case occurs with probability around 256 -- 2**Machine_Emin, and the expected number of calls to integer-valued 257 -- Random is 1. For another discussion of the issues addressed by this 258 -- process, see Allen Downey's unpublished paper at 259 -- http://allendowney.com/research/rand/downey07randfloat.pdf. 260 261 if Real'Machine_Radix /= 2 then 262 return Real'Machine 263 (Real (Unsigned'(Random (Gen))) * 2.0**(-Unsigned'Size)); 264 265 else 266 declare 267 type Bit_Count is range 0 .. 4; 268 269 subtype T is Real'Base; 270 271 Trailing_Ones : constant array (Unsigned_32 range 0 .. 15) 272 of Bit_Count := 273 (2#00000# => 0, 2#00001# => 1, 2#00010# => 0, 2#00011# => 2, 274 2#00100# => 0, 2#00101# => 1, 2#00110# => 0, 2#00111# => 3, 275 2#01000# => 0, 2#01001# => 1, 2#01010# => 0, 2#01011# => 2, 276 2#01100# => 0, 2#01101# => 1, 2#01110# => 0, 2#01111# => 4); 277 278 Pow_Tab : constant array (Bit_Count range 0 .. 3) of Real 279 := (0 => 2.0**(0 - T'Machine_Mantissa), 280 1 => 2.0**(-1 - T'Machine_Mantissa), 281 2 => 2.0**(-2 - T'Machine_Mantissa), 282 3 => 2.0**(-3 - T'Machine_Mantissa)); 283 284 Extra_Bits : constant Natural := 285 (Unsigned'Size - T'Machine_Mantissa + 1); 286 -- Random bits left over after selecting mantissa 287 288 Mantissa : Unsigned; 289 290 X : Real; -- Scaled mantissa 291 R : Unsigned_32; -- Supply of random bits 292 R_Bits : Natural; -- Number of bits left in R 293 K : Bit_Count; -- Next decrement to exponent 294 295 begin 296 Mantissa := Random (Gen) / 2**Extra_Bits; 297 R := Unsigned_32 (Mantissa mod 2**Extra_Bits); 298 R_Bits := Extra_Bits; 299 X := Real (2**(T'Machine_Mantissa - 1) + Mantissa); -- Exact 300 301 if Extra_Bits < 4 and then R < 2 ** Extra_Bits - 1 then 302 303 -- We got lucky and got a zero in our few extra bits 304 305 K := Trailing_Ones (R); 306 307 else 308 Find_Zero : loop 309 310 -- R has R_Bits unprocessed random bits, a multiple of 4. 311 -- X needs to be halved for each trailing one bit. The 312 -- process stops as soon as a 0 bit is found. If R_Bits 313 -- becomes zero, reload R. 314 315 -- Process 4 bits at a time for speed: the two iterations 316 -- on average with three tests each was still too slow, 317 -- probably because the branches are not predictable. 318 -- This loop now will only execute once 94% of the cases, 319 -- doing more bits at a time will not help. 320 321 while R_Bits >= 4 loop 322 K := Trailing_Ones (R mod 16); 323 324 exit Find_Zero when K < 4; -- Exits 94% of the time 325 326 R_Bits := R_Bits - 4; 327 X := X / 16.0; 328 R := R / 16; 329 end loop; 330 331 -- Do not allow us to loop endlessly even in the (very 332 -- unlikely) case that Random (Gen) keeps yielding all ones. 333 334 exit Find_Zero when X = 0.0; 335 R := Random (Gen); 336 R_Bits := 32; 337 end loop Find_Zero; 338 end if; 339 340 -- K has the count of trailing ones not reflected yet in X. The 341 -- following multiplication takes care of that, as well as the 342 -- correction to move the radix point to the left of the mantissa. 343 -- Doing it at the end avoids repeated rounding errors in the 344 -- exceedingly unlikely case of ever having a subnormal result. 345 346 X := X * Pow_Tab (K); 347 348 -- The smallest value in each binade is rounded to by 0.75 of 349 -- the span of real numbers as its next larger neighbor, and 350 -- 1.0 is rounded to by half of the span of real numbers as its 351 -- next smaller neighbor. To account for this, when we encounter 352 -- the smallest number in a binade, we substitute the smallest 353 -- value in the next larger binade with probability 1/2. 354 355 if Mantissa = 0 and then Unsigned_32'(Random (Gen)) mod 2 = 0 then 356 X := 2.0 * X; 357 end if; 358 359 return X; 360 end; 361 end if; 362 end Random_Float_Template; 363 364 ------------ 365 -- Random -- 366 ------------ 367 368 function Random (Gen : Generator) return Float is 369 function F is new Random_Float_Template (Unsigned_32, Float); 370 begin 371 return F (Gen); 372 end Random; 373 374 function Random (Gen : Generator) return Long_Float is 375 function F is new Random_Float_Template (Unsigned_64, Long_Float); 376 begin 377 return F (Gen); 378 end Random; 379 380 function Random (Gen : Generator) return Unsigned_64 is 381 begin 382 return Shift_Left (Unsigned_64 (Unsigned_32'(Random (Gen))), 32) 383 or Unsigned_64 (Unsigned_32'(Random (Gen))); 384 end Random; 385 386 --------------------- 387 -- Random_Discrete -- 388 --------------------- 389 390 function Random_Discrete 391 (Gen : Generator; 392 Min : Result_Subtype := Default_Min; 393 Max : Result_Subtype := Result_Subtype'Last) return Result_Subtype 394 is 395 begin 396 if Max = Min then 397 return Max; 398 399 elsif Max < Min then 400 raise Constraint_Error; 401 402 elsif Result_Subtype'Base'Size > 32 then 403 declare 404 -- In the 64-bit case, we have to be careful, since not all 64-bit 405 -- unsigned values are representable in GNAT's root_integer type. 406 -- Ignore different-size warnings here since GNAT's handling 407 -- is correct. 408 409 pragma Warnings ("Z"); 410 function Conv_To_Unsigned is 411 new Unchecked_Conversion (Result_Subtype'Base, Unsigned_64); 412 function Conv_To_Result is 413 new Unchecked_Conversion (Unsigned_64, Result_Subtype'Base); 414 pragma Warnings ("z"); 415 416 N : constant Unsigned_64 := 417 Conv_To_Unsigned (Max) - Conv_To_Unsigned (Min) + 1; 418 419 X, Slop : Unsigned_64; 420 421 begin 422 if N = 0 then 423 return Conv_To_Result (Conv_To_Unsigned (Min) + Random (Gen)); 424 425 else 426 Slop := Unsigned_64'Last rem N + 1; 427 428 loop 429 X := Random (Gen); 430 exit when Slop = N or else X <= Unsigned_64'Last - Slop; 431 end loop; 432 433 return Conv_To_Result (Conv_To_Unsigned (Min) + X rem N); 434 end if; 435 end; 436 437 elsif Result_Subtype'Pos (Max) - Result_Subtype'Pos (Min) = 438 2 ** 32 - 1 439 then 440 return Result_Subtype'Val 441 (Result_Subtype'Pos (Min) + Unsigned_32'Pos (Random (Gen))); 442 else 443 declare 444 N : constant Unsigned_32 := 445 Unsigned_32 (Result_Subtype'Pos (Max) - 446 Result_Subtype'Pos (Min) + 1); 447 Slop : constant Unsigned_32 := Unsigned_32'Last rem N + 1; 448 X : Unsigned_32; 449 450 begin 451 loop 452 X := Random (Gen); 453 exit when Slop = N or else X <= Unsigned_32'Last - Slop; 454 end loop; 455 456 return 457 Result_Subtype'Val 458 (Result_Subtype'Pos (Min) + Unsigned_32'Pos (X rem N)); 459 end; 460 end if; 461 end Random_Discrete; 462 463 ------------------ 464 -- Random_Float -- 465 ------------------ 466 467 function Random_Float (Gen : Generator) return Result_Subtype is 468 begin 469 if Result_Subtype'Base'Digits > Float'Digits then 470 return Result_Subtype'Machine (Result_Subtype 471 (Long_Float'(Random (Gen)))); 472 else 473 return Result_Subtype'Machine (Result_Subtype 474 (Float'(Random (Gen)))); 475 end if; 476 end Random_Float; 477 478 ----------- 479 -- Reset -- 480 ----------- 481 482 procedure Reset (Gen : Generator) is 483 begin 484 Init (Gen, Unsigned_32'Mod (Random_Seed.Get_Seed)); 485 end Reset; 486 487 procedure Reset (Gen : Generator; Initiator : Integer_32) is 488 begin 489 Init (Gen, To_Unsigned (Initiator)); 490 end Reset; 491 492 procedure Reset (Gen : Generator; Initiator : Unsigned_32) is 493 begin 494 Init (Gen, Initiator); 495 end Reset; 496 497 procedure Reset (Gen : Generator; Initiator : Integer) is 498 begin 499 -- This is probably an unnecessary precaution against future change, but 500 -- since the test is a static expression, no extra code is involved. 501 502 if Integer'Size <= 32 then 503 Init (Gen, To_Unsigned (Integer_32 (Initiator))); 504 505 else 506 declare 507 Initiator1 : constant Unsigned_64 := 508 To_Unsigned (Integer_64 (Initiator)); 509 Init0 : constant Unsigned_32 := 510 Unsigned_32 (Initiator1 mod 2 ** 32); 511 Init1 : constant Unsigned_32 := 512 Unsigned_32 (Shift_Right (Initiator1, 32)); 513 begin 514 Reset (Gen, Initialization_Vector'(Init0, Init1)); 515 end; 516 end if; 517 end Reset; 518 519 procedure Reset (Gen : Generator; Initiator : Initialization_Vector) is 520 G : Generator renames Gen.Writable.Self.all; 521 I, J : Integer; 522 523 begin 524 Init (G, Seed1); 525 I := 1; 526 J := 0; 527 528 if Initiator'Length > 0 then 529 for K in reverse 1 .. Integer'Max (N, Initiator'Length) loop 530 G.S (I) := 531 (G.S (I) xor ((G.S (I - 1) 532 xor Shift_Right (G.S (I - 1), 30)) * Mult1)) 533 + Initiator (J + Initiator'First) + Unsigned_32 (J); 534 535 I := I + 1; 536 J := J + 1; 537 538 if I >= N then 539 G.S (0) := G.S (N - 1); 540 I := 1; 541 end if; 542 543 if J >= Initiator'Length then 544 J := 0; 545 end if; 546 end loop; 547 end if; 548 549 for K in reverse 1 .. N - 1 loop 550 G.S (I) := 551 (G.S (I) xor ((G.S (I - 1) 552 xor Shift_Right (G.S (I - 1), 30)) * Mult2)) 553 - Unsigned_32 (I); 554 I := I + 1; 555 556 if I >= N then 557 G.S (0) := G.S (N - 1); 558 I := 1; 559 end if; 560 end loop; 561 562 G.S (0) := Upper_Mask; 563 end Reset; 564 565 procedure Reset (Gen : Generator; From_State : Generator) is 566 G : Generator renames Gen.Writable.Self.all; 567 begin 568 G.S := From_State.S; 569 G.I := From_State.I; 570 end Reset; 571 572 procedure Reset (Gen : Generator; From_State : State) is 573 G : Generator renames Gen.Writable.Self.all; 574 begin 575 G.I := 0; 576 G.S := From_State; 577 end Reset; 578 579 procedure Reset (Gen : Generator; From_Image : String) is 580 G : Generator renames Gen.Writable.Self.all; 581 begin 582 G.I := 0; 583 584 for J in 0 .. N - 1 loop 585 G.S (J) := Extract_Value (From_Image, J); 586 end loop; 587 end Reset; 588 589 ---------- 590 -- Save -- 591 ---------- 592 593 procedure Save (Gen : Generator; To_State : out State) is 594 Gen2 : Generator; 595 596 begin 597 if Gen.I = N then 598 Init (Gen2, 5489); 599 To_State := Gen2.S; 600 601 else 602 To_State (0 .. N - 1 - Gen.I) := Gen.S (Gen.I .. N - 1); 603 To_State (N - Gen.I .. N - 1) := Gen.S (0 .. Gen.I - 1); 604 end if; 605 end Save; 606 607 ----------- 608 -- Image -- 609 ----------- 610 611 function Image (Of_State : State) return String is 612 Result : Image_String; 613 614 begin 615 Result := (others => ' '); 616 617 for J in Of_State'Range loop 618 Insert_Image (Result, J, Of_State (J)); 619 end loop; 620 621 return Result; 622 end Image; 623 624 function Image (Gen : Generator) return String is 625 Result : Image_String; 626 627 begin 628 Result := (others => ' '); 629 for J in 0 .. N - 1 loop 630 Insert_Image (Result, J, Gen.S ((J + Gen.I) mod N)); 631 end loop; 632 633 return Result; 634 end Image; 635 636 ----------- 637 -- Value -- 638 ----------- 639 640 function Value (Coded_State : String) return State is 641 Gen : Generator; 642 S : State; 643 begin 644 Reset (Gen, Coded_State); 645 Save (Gen, S); 646 return S; 647 end Value; 648 649 ---------- 650 -- Init -- 651 ---------- 652 653 procedure Init (Gen : Generator; Initiator : Unsigned_32) is 654 G : Generator renames Gen.Writable.Self.all; 655 begin 656 G.S (0) := Initiator; 657 658 for I in 1 .. N - 1 loop 659 G.S (I) := 660 (G.S (I - 1) xor Shift_Right (G.S (I - 1), 30)) * Mult0 661 + Unsigned_32 (I); 662 end loop; 663 664 G.I := 0; 665 end Init; 666 667 ------------------ 668 -- Insert_Image -- 669 ------------------ 670 671 procedure Insert_Image 672 (S : in out Image_String; 673 Index : Integer; 674 V : State_Val) 675 is 676 Value : constant String := State_Val'Image (V); 677 begin 678 S (Index * 11 + 1 .. Index * 11 + Value'Length) := Value; 679 end Insert_Image; 680 681 ------------------- 682 -- Extract_Value -- 683 ------------------- 684 685 function Extract_Value (S : String; Index : Integer) return State_Val is 686 Start : constant Integer := S'First + Index * Image_Numeral_Length; 687 begin 688 return State_Val'Value (S (Start .. Start + Image_Numeral_Length - 1)); 689 end Extract_Value; 690 691end System.Random_Numbers; 692