import java.math.BigInteger;
import java.math.BigDecimal;

class Fibonacci4
{
    /** Using exact integer arithmetic, print N_Terms ascending
    members of the Fibonacci sequence, prefixed by their term numbers,
    and followed by the ratio of successive terms, to demonstrate the
    1.618...^n growth (the ratio approaches the golden ratio, (1 +
    sqrt(5))/2 = 1.6180339887498949, and reaches it (to 64-bit machine
    precision) at 41 terms: the fourth item on each line is the
    difference from the golden ratio).

    Java's BigDecimal package, which is intended for simple
    high-precision currency calculations, does not provide elementary
    functions, such as sqrt(), so we supply a 100D-string
    representation for the golden_ratio. */

    private static final int Fractional_Digits = 50; //
    private static final int N_Terms = 200; //

    static final BigDecimal golden_ratio = new BigDecimal("1.618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391138");

    public static void main(String[] args)
    {
	BigInteger lo = BigInteger.valueOf(1L);
	BigInteger hi = BigInteger.valueOf(1L);
	int n = 1;

	System.out.print(n);
	System.out.print("\t");
	System.out.println(lo);

	while (n < N_Terms)
	{
	    n++;
	    System.out.print(n);
	    System.out.print("\t");
	    System.out.print(hi);
	    System.out.print("\t");
	    BigDecimal ratio = new BigDecimal(hi);
	    BigDecimal den = new BigDecimal(lo);
	    ratio = ratio.divide(den, Fractional_Digits, ratio.ROUND_HALF_DOWN);
	    System.out.print(ratio);
	    System.out.print("\t");
	    System.out.println(ratio.subtract(golden_ratio).setScale(Fractional_Digits,
								     ratio.ROUND_HALF_DOWN));
	    hi = lo.add(hi);
	    lo = hi.subtract(lo);
	}
    }
}