#/***********************************************************
#    fib.rb -- Fibonacci (フィボナッチ) 数列
#***********************************************************/

def fib1( n )
    return ((1 + Math::sqrt(5)) / 2)** n / Math::sqrt(5) + 0.5
end

def fib2( n )
    a = 1;  b = 1;  c = 0;  x = 1;  y = 0;  n -= 1
    while (n > 0) 
        if (n % 2) == 1
            x1 = x;  y1 = y
            x = a * x1 + b * y1;  y = b * x1 + c * y1
        end
        n /= 2
        a1 = a;  b1 = b;  c1 = c
        a = a1 * a1 + b1 * b1
        b = b1 * (a1 + c1)
        c = b1 * b1 + c1 * c1
    end
    return x
end

a = 1;  b = 0
while (a < 100) 
    printf(" %d", a)
    t = a + b;  b = a;  a = t
end
printf("\n")

a = 1;  b = 0
while (a < 100) 
    printf(" %d", a)
    a += b;  b = a - b
end
printf("\n")

for i in 1..11; printf(" %d", fib1(i)); end
printf("\n")

for i in 1..11; printf(" %d", fib2(i)); end
printf("\n")

exit 0