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多倍長黄金比を求める (SQR(5)+1)/2=1.618033...
計算式に
(1-X)^(-.5)=1+(1/2)*X+(1*3)/(2*4)*X^2+(1*3*5)/(2*4*6)*X^3+...
を使用し、以下の関係式
SQR(5)= 6460 / 2889 * (1 - 1 / 8346321)^(-.5)
を使って黄金比を求める。
PUBLIC NUMERIC KETA,EPS,SIGN
INPUT PROMPT "桁数=":KETA
LET KETA=INT(KETA/4)
LET EPS=2
LET BIAS=0
LET KETA=KETA+EPS
LET SIGN=-BIAS-1
DIM A(-BIAS-1 TO KETA),S(-BIAS-1 TO KETA),T(-BIAS-1 TO KETA)
LET A(0)=1
LET S(0)=1
LET N=1
DO
MAT A=(2*N-1)*A
FOR I = 0 TO KETA - 1
LET R = A(I) - INT(A(I)/16692642/N)*(16692642*N)
LET A(I) = INT(A(I) /16692642/N)
LET A(I + 1) = A(I + 1) + R * 10000
NEXT I
LET A(KETA) = INT(A(KETA)/16692642/N)
MAT S=S+A
FOR I = KETA TO 0 STEP -1
IF S(I) >= 10000 THEN
LET R = INT(S(I) / 10000)
LET S(I) = S(I) - R * 10000
LET S(I-1) = S(I-1) + R
END IF
NEXT I
LET FL=0
FOR I=0 TO KETA
IF S(I)<>T(I) THEN
LET T(I)=S(I)
LET FL=1
LET N=N+1
EXIT FOR
END IF
NEXT I
IF FL=0 THEN EXIT DO
LOOP
MAT S=6460*S
FOR I = KETA TO 0 STEP -1
IF S(I) >= 10000 THEN
LET R = INT(S(I) / 10000)
LET S(I) = S(I) - R * 10000
LET S(I-1) = S(I-1) + R
END IF
NEXT I
FOR I = 0 TO KETA - 1
LET R = S(I) - INT(S(I)/2889)*2889
LET S(I) = INT(S(I)/2889)
LET S(I + 1) = S(I + 1) + R * 10000
NEXT I
LET S(KETA) = INT(S(KETA)/2889)
LET S(0)=S(0)+1
FOR I = 0 TO KETA - 1
LET R = S(I) - INT(S(I)/2)*2
LET S(I) = INT(S(I)/2)
LET S(I + 1) = S(I + 1) + R * 10000
NEXT I
LET S(KETA) = INT(S(KETA)/2)
CALL DISPLAY(S)
END
EXTERNAL SUB DISPLAY(X())
FOR K=-BIAS TO 0
IF X(K)<>0 THEN EXIT FOR
NEXT K
IF K > 0 THEN LET K=0
IF X(SIGN) = -1 THEN PRINT "- ";
PRINT STR$(X(K));" ";
IF K=0 THEN PRINT "."
FOR I=K+1 TO KETA-EPS
LET L=L+1
PRINT RIGHT$("000"&STR$(X(I)),4);" ";
IF I=0 THEN
PRINT "."
LET L=0
END IF
IF MOD(L,25)=0 THEN PRINT
NEXT I
PRINT
END SUB
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