File:  [Local Repository] / imach / src / random.alw
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Sat Feb 3 23:37:11 2024 UTC (9 months, 1 week ago) by brouard
Branches: MAIN
CVS tags: HEAD
Summary: Random from Brent in Algol W

COMMENT:	RANDOM NUMBER GENERATOR
                ***********************

  PROCEDURE RANDOM RETURNS A LONG REAL RANDOM NUMBER UNIFORMLY
      DISTRIBUTED IN (0,1) (INCLUDING 0 BUT NOT 1),
      RANINIT(R) WITH R ANY INTEGER MUST BE CALLED FOR
      INITIALIZATION BEFORE THE FIRST CALL TO RANDOM, AND THE
      DECLARATIONS OF RAN1, RAN2 AND RAN3 MUST BE GLOBAL,
      THE ALGORITHM RETURNS X(N)/2**56, WHERE
                   X(N) = X(N-1) + X(N-127) (MOO 2**56),
      SINCE 1 + X + X**127 IS PRIMITIVE (MOD 2), THE PERIOD IS AT
      LEAST 2**127 - 1 > 10**38, SEE KNUTH (1969), PP. 26, 34, 464,
      X(N) IS STORED IN A LONG REAL WORD AS
      RAN3 = X(N)/2**56 - 1/2, AND ALL FLOATING POINT ARITHMETIC
      IS EXACT;

  LONG REAL PROCEDURE RANDOM(INTEGER VALUE NAUGHT);
  BEGIN
    LONG REAL RAN1; INTEGER RAN2; LONG REAL ARRAY RAN3 (0::126);
    INTEGER R; LOGICAL INIT;
    INIT := FALSE;
    IF INIT THEN GO TO L3;
    R := ABS(NAUGHT) REM 8190 + 1;
    RAN2 := 127; WHILE RAN2 > 0 DO
    BEGIN RAN2 := RAN2 - 1; RAN1 := -2L**55;
      FOR I := 1 UNTIL 7 DO
      BEGIN R := (1756*R) REM 8191;
        RAN1 := (RAN1 + (R DIV 32) )*( 1/256) ;
      END;
      RAN3 (RAN2) := RAN1
    END;
    INIT := TRUE;
  L3: RAN2 := IF RAN2 = 0 THEN 126 ELSE RAN2 - 1;
    RAN1 := RAN1 + RAN3 (RAN2);
    RAN3 (RAN2) := RAN1 := IF RAN1 < 0L THEN RAN1 + 0.5L
                        ELSE RAN1 - 0.5L;
    RAN1 + 0.5L
  END RANDOM.

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