File: PIXAKT.PS of Tape: Various/Decus/decus-3

(Source file text) 

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PROGRAM PIIIIIIIIIIII(INPUT,OUTPUT);


(*)
(   BERECHNUNG DER ZAHL  PI  AUF BIS ZU 1000 KOMMASTELLEN GENAU
(   AUS
(
(           PI = 20 * ARCTAN(1/7)  +  8 * ARCTAN(3/79)
(
(
(   UEBER DIE REIHENENTWICKLUNG
(
(
(                 T             2     T^2       2   4     T^2
(   ARCTAN(T) = ----- * ( 1  +  - * (-----)  +  - * - * (-----)^2  +
(               1+T^2           3    1+T^2      3   5    1+T^2
(
(
(                2   4   6     T^2
(             +  - * - * - * (-----)^3  +  .......  )
(                3   5   7    1+T^2
(
(*)


  CONST BASE (* OF ARITHMETIC *) = 100000  (* DON'T CHANGE *);


  TYPE  LONGNUMBER = ARRAY[0..205] OF INTEGER;


  VAR   NUMBEROFDIGITS, N, I, AFIRST, BFIRST, LAST,
        CARRY, DIGIT, POWER, AMUL, BMUL, ADIV, BDIV: INTEGER;

        A, B, PI: LONGNUMBER;


BEGIN
    READ(NUMBEROFDIGITS);
    AFIRST := 0;  BFIRST := 1;  LAST := NUMBEROFDIGITS DIV 5 + 4;

    (*)
    (   AUFSTELLEN DER ANFANGSGLIEDER BEIDER REIHEN
    (   UND DES ANFANGSWERTES DER SUMME:
    (*)

    N := 0;
     A[0] := 2;  A[1] := 80000 (* OF 2.80000 *);
     B[0] := 0;  B[1] := 30336 (* OF 0.30336 *);
    PI[0] := 3; PI[1] := 10336 (* OF 3.10336 *);
    FOR I := 2 TO LAST DO
        BEGIN A[I] := 0;  B[I] := 0;  PI[I] := 0 END;
    A[LAST+1] := BASE  (* GUARD *);
    B[LAST+1] := BASE  (* GUARD *);


    REPEAT N := N + 1;

        (*)
        (   BERECHNUNG DES N-TEN GLIEDES DER ERSTEN REIHE:
        (
        (           A <=== A * AMUL / ADIV
        (
        (*)

        AMUL := N;
        I := LAST+1;  CARRY := 0;
        WHILE (AFIRST<I) OR (CARRY<>0) DO
          BEGIN
            I := I - 1;
            DIGIT := AMUL*A[I] + CARRY;
            A[I]  := DIGIT MOD BASE;
            CARRY := DIGIT DIV BASE
          END;
        AFIRST := I;

        ADIV := (N+N + 1)*25;
        CARRY := 0;
        FOR I := AFIRST TO LAST DO
          BEGIN
            DIGIT := CARRY*BASE + A[I];
            A[I]  := DIGIT DIV ADIV;
            CARRY := DIGIT MOD ADIV
          END;
        WHILE A[AFIRST]=0 DO AFIRST := AFIRST + 1;


        (*)
        (   BERECHNUNG DES N-TEN GLIEDES DER ZWEITEN REIHE:
        (
        (           B <=== B * BMUL / BDIV
        (
        (*)

        BMUL := 288*N  (* INCLUDES DIVISION BY 100000 *);
        I := LAST;  CARRY := (BMUL*B[LAST]) DIV BASE;
        WHILE (BFIRST<I) OR (CARRY<>0) DO
          BEGIN
            I := I - 1;
            DIGIT := BMUL*B[I] + CARRY;
            B[I+1]:= DIGIT MOD BASE;
            CARRY := DIGIT DIV BASE
          END;
        B[I] := 0;  BFIRST := I+1;

        BDIV := N+N + 1;
        CARRY := 0;
        FOR I := BFIRST TO LAST DO
          BEGIN
            DIGIT := CARRY*BASE + B[I];
            B[I]  := DIGIT DIV BDIV;
            CARRY := DIGIT MOD BDIV
          END;
        IF B[BFIRST]=0 THEN BFIRST := BFIRST + 1;

        (*)
        (   AUFSUMMIERUNG ZUR ZAHL PI:
        (
        (          PI <=== PI + A + B
        (
        (*)

        I := LAST;  CARRY := 0;
        WHILE (AFIRST<=I) OR (CARRY<>0) DO
          BEGIN
            DIGIT := PI[I] + A[I] + B[I] + CARRY;  CARRY := 0;
            WHILE DIGIT>=BASE DO BEGIN
                                   DIGIT := DIGIT - BASE;
                                   CARRY := CARRY + 1
                                END;
            PI[I] := DIGIT;
            I := I - 1
          END

    UNTIL AFIRST>LAST;


    (*)
    (   AUSGABE:
    (*)

    WRITELN; WRITE("PI = 3.":10);
    FOR I := 1 TO LAST-4 DO
      BEGIN
        DIGIT := PI[I];  POWER := BASE;
        REPEAT POWER := POWER DIV 10;
            WRITE(DIGIT DIV POWER :1);
            DIGIT := DIGIT MOD POWER
        UNTIL POWER=1;
        IF I MOD 10 = 0 THEN BEGIN WRITELN; WRITE(" ":10) END
      END;
    WRITELN
END.

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