| 1 | PROGRAM PIIIIIIIIIIII(INPUT,OUTPUT); |
| 2 | |
| 3 | |
| 4 | (*) |
| 5 | ( BERECHNUNG DER ZAHL PI AUF BIS ZU 1000 KOMMASTELLEN GENAU |
| 6 | ( AUS |
| 7 | ( |
| 8 | ( PI = 20 * ARCTAN(1/7) + 8 * ARCTAN(3/79) |
| 9 | ( |
| 10 | ( |
| 11 | ( UEBER DIE REIHENENTWICKLUNG |
| 12 | ( |
| 13 | ( |
| 14 | ( T 2 T^2 2 4 T^2 |
| 15 | ( ARCTAN(T) = ----- * ( 1 + - * (-----) + - * - * (-----)^2 + |
| 16 | ( 1+T^2 3 1+T^2 3 5 1+T^2 |
| 17 | ( |
| 18 | ( |
| 19 | ( 2 4 6 T^2 |
| 20 | ( + - * - * - * (-----)^3 + ....... ) |
| 21 | ( 3 5 7 1+T^2 |
| 22 | ( |
| 23 | (*) |
| 24 | |
| 25 | |
| 26 | CONST BASE (* OF ARITHMETIC *) = 100000 (* DON'T CHANGE *); |
| 27 | |
| 28 | |
| 29 | TYPE LONGNUMBER = ARRAY[0..205] OF INTEGER; |
| 30 | |
| 31 | |
| 32 | VAR NUMBEROFDIGITS, N, I, AFIRST, BFIRST, LAST, |
| 33 | CARRY, DIGIT, POWER, AMUL, BMUL, ADIV, BDIV: INTEGER; |
| 34 | |
| 35 | A, B, PI: LONGNUMBER; |
| 36 | |
| 37 | |
| 38 | BEGIN |
| 39 | READ(NUMBEROFDIGITS); |
| 40 | AFIRST := 0; BFIRST := 1; LAST := NUMBEROFDIGITS DIV 5 + 4; |
| 41 | |
| 42 | (*) |
| 43 | ( AUFSTELLEN DER ANFANGSGLIEDER BEIDER REIHEN |
| 44 | ( UND DES ANFANGSWERTES DER SUMME: |
| 45 | (*) |
| 46 | |
| 47 | N := 0; |
| 48 | A[0] := 2; A[1] := 80000 (* OF 2.80000 *); |
| 49 | B[0] := 0; B[1] := 30336 (* OF 0.30336 *); |
| 50 | PI[0] := 3; PI[1] := 10336 (* OF 3.10336 *); |
| 51 | FOR I := 2 TO LAST DO |
| 52 | BEGIN A[I] := 0; B[I] := 0; PI[I] := 0 END; |
| 53 | A[LAST+1] := BASE (* GUARD *); |
| 54 | B[LAST+1] := BASE (* GUARD *); |
| 55 | |
| 56 | |
| 57 | REPEAT N := N + 1; |
| 58 | |
| 59 | (*) |
| 60 | ( BERECHNUNG DES N-TEN GLIEDES DER ERSTEN REIHE: |
| 61 | ( |
| 62 | ( A <=== A * AMUL / ADIV |
| 63 | ( |
| 64 | (*) |
| 65 | |
| 66 | AMUL := N; |
| 67 | I := LAST+1; CARRY := 0; |
| 68 | WHILE (AFIRST<I) OR (CARRY<>0) DO |
| 69 | BEGIN |
| 70 | I := I - 1; |
| 71 | DIGIT := AMUL*A[I] + CARRY; |
| 72 | A[I] := DIGIT MOD BASE; |
| 73 | CARRY := DIGIT DIV BASE |
| 74 | END; |
| 75 | AFIRST := I; |
| 76 | |
| 77 | ADIV := (N+N + 1)*25; |
| 78 | CARRY := 0; |
| 79 | FOR I := AFIRST TO LAST DO |
| 80 | BEGIN |
| 81 | DIGIT := CARRY*BASE + A[I]; |
| 82 | A[I] := DIGIT DIV ADIV; |
| 83 | CARRY := DIGIT MOD ADIV |
| 84 | END; |
| 85 | WHILE A[AFIRST]=0 DO AFIRST := AFIRST + 1; |
| 86 | |
| 87 | |
| 88 | (*) |
| 89 | ( BERECHNUNG DES N-TEN GLIEDES DER ZWEITEN REIHE: |
| 90 | ( |
| 91 | ( B <=== B * BMUL / BDIV |
| 92 | ( |
| 93 | (*) |
| 94 | |
| 95 | BMUL := 288*N (* INCLUDES DIVISION BY 100000 *); |
| 96 | I := LAST; CARRY := (BMUL*B[LAST]) DIV BASE; |
| 97 | WHILE (BFIRST<I) OR (CARRY<>0) DO |
| 98 | BEGIN |
| 99 | I := I - 1; |
| 100 | DIGIT := BMUL*B[I] + CARRY; |
| 101 | B[I+1]:= DIGIT MOD BASE; |
| 102 | CARRY := DIGIT DIV BASE |
| 103 | END; |
| 104 | B[I] := 0; BFIRST := I+1; |
| 105 | |
| 106 | BDIV := N+N + 1; |
| 107 | CARRY := 0; |
| 108 | FOR I := BFIRST TO LAST DO |
| 109 | BEGIN |
| 110 | DIGIT := CARRY*BASE + B[I]; |
| 111 | B[I] := DIGIT DIV BDIV; |
| 112 | CARRY := DIGIT MOD BDIV |
| 113 | END; |
| 114 | IF B[BFIRST]=0 THEN BFIRST := BFIRST + 1; |
| 115 | |
| 116 | (*) |
| 117 | ( AUFSUMMIERUNG ZUR ZAHL PI: |
| 118 | ( |
| 119 | ( PI <=== PI + A + B |
| 120 | ( |
| 121 | (*) |
| 122 | |
| 123 | I := LAST; CARRY := 0; |
| 124 | WHILE (AFIRST<=I) OR (CARRY<>0) DO |
| 125 | BEGIN |
| 126 | DIGIT := PI[I] + A[I] + B[I] + CARRY; CARRY := 0; |
| 127 | WHILE DIGIT>=BASE DO BEGIN |
| 128 | DIGIT := DIGIT - BASE; |
| 129 | CARRY := CARRY + 1 |
| 130 | END; |
| 131 | PI[I] := DIGIT; |
| 132 | I := I - 1 |
| 133 | END |
| 134 | |
| 135 | UNTIL AFIRST>LAST; |
| 136 | |
| 137 | |
| 138 | (*) |
| 139 | ( AUSGABE: |
| 140 | (*) |
| 141 | |
| 142 | WRITELN; WRITE("PI = 3.":10); |
| 143 | FOR I := 1 TO LAST-4 DO |
| 144 | BEGIN |
| 145 | DIGIT := PI[I]; POWER := BASE; |
| 146 | REPEAT POWER := POWER DIV 10; |
| 147 | WRITE(DIGIT DIV POWER :1); |
| 148 | DIGIT := DIGIT MOD POWER |
| 149 | UNTIL POWER=1; |
| 150 | IF I MOD 10 = 0 THEN BEGIN WRITELN; WRITE(" ":10) END |
| 151 | END; |
| 152 | WRITELN |
| 153 | END. |